messages listlengths 3 3 | topic stringclasses 1
value | subtopic stringclasses 3
values |
|---|---|---|
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A angle-angle-side triangle has angles $\\frac{9 \\pi }{20}$ and $\\frac{23 \\pi }{60}$ and a side of length $10$. Determine the area, circumradius, inradius, and sem... | geometry | triangles |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A angle-angle-side triangle has angles $76 {}^{\\circ}$ and $102 {}^{\\circ}$ and a side of length $4.25$. Determine the locations of the triangle's vertices and the ... | geometry | triangles |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A side-angle-side triangle has sides $6.06$ and $8.06$ and an angle $79 {}^{\\circ}$. Determine points to define lines for the triangle's altitude, cevian, median, an... | geometry | triangles |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A angle-angle-side triangle has angles $38 {}^{\\circ}$ and $108 {}^{\\circ}$ and a side of length $2.5$. Determine points to define lines for the triangle's altitude... | geometry | triangles |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A triangle has sides $10, \\frac{13}{2}, \\frac{27}{2}$. Determine the locations of the triangle's vertices and the three interior angles."
},
{
"role": "assi... | geometry | triangles |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A angle-side-angle triangle has angle $\\frac{19 \\pi }{30}$, a side of length $10.$ and an angle of measure $\\frac{13 \\pi }{45}$. Determine the locations of the tr... | geometry | triangles |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A triangle has sides $7, 3, 6$. Determine points to define lines for the triangle's altitude, cevian, median, and symmedian lines."
},
{
"role": "assistant",
... | geometry | triangles |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A triangle has sides $5.5, 11.5, 11.$. Determine the area, circumradius, inradius, and semiperimeter of the triangle."
},
{
"role": "assistant",
"content"... | geometry | triangles |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A angle-angle-side triangle has angles $145 {}^{\\circ}$ and $13 {}^{\\circ}$ and a side of length $6$. Determine the locations of the triangle's vertices and the thr... | geometry | triangles |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A angle-side-angle triangle has angle $\\frac{47 \\pi }{180}$, a side of length $9$ and an angle of measure $\\frac{23 \\pi }{36}$. Determine points to define lines f... | geometry | triangles |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A side-angle-side triangle has sides $9$ and $9$ and an angle $73 {}^{\\circ}$. Determine the locations of the triangle's vertices and the three interior angles."
}... | geometry | triangles |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A angle-side-angle triangle has angle $160 {}^{\\circ}$, a side of length $13$ and an angle of measure $5 {}^{\\circ}$. Determine the area, circumradius, inradius, an... | geometry | triangles |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A side-angle-side triangle has sides $7.5$ and $9.5$ and an angle $\\frac{11 \\pi }{90}$. Determine the centroid, circumcenter, incenter, orthocenter, nine point cent... | geometry | triangles |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A angle-side-angle triangle has angle $\\frac{11 \\pi }{36}$, a side of length $3.5$ and an angle of measure $\\frac{3 \\pi }{5}$. Determine points to define lines fo... | geometry | triangles |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A side-angle-side triangle has sides $9.$ and $8.$ and an angle $\\frac{103 \\pi }{180}$. Determine the locations of the triangle's vertices and the three interior an... | geometry | triangles |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A angle-angle-side triangle has angles $147 {}^{\\circ}$ and $12 {}^{\\circ}$ and a side of length $6.69$. Determine points to define lines for the triangle's altitud... | geometry | triangles |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A angle-angle-side triangle has angles $152 {}^{\\circ}$ and $6 {}^{\\circ}$ and a side of length $9$. Determine the locations of the triangle's vertices and the thre... | geometry | triangles |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A triangle has sides $11.75, 8., 17.$. Determine the centroid, circumcenter, incenter, orthocenter, nine point center, and symmedian point of the triangle."
},
{
... | geometry | triangles |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A angle-angle-side triangle has angles $167 {}^{\\circ}$ and $10 {}^{\\circ}$ and a side of length $2$. Determine points to define lines for the triangle's altitude, ... | geometry | triangles |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A triangle has sides $14.49, 6.68, 16.64$. Determine the centroid, circumcenter, incenter, orthocenter, nine point center, and symmedian point of the triangle."
},
... | geometry | triangles |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A angle-angle-side triangle has angles $126 {}^{\\circ}$ and $6 {}^{\\circ}$ and a side of length $7.5$. Determine the centroid, circumcenter, incenter, orthocenter, ... | geometry | triangles |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A angle-side-angle triangle has angle $\\frac{19 \\pi }{180}$, a side of length $13.5$ and an angle of measure $\\frac{\\pi }{9}$. Determine points to define lines fo... | geometry | triangles |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A triangle has sides $6.5, 12., 16.5$. Determine the locations of the triangle's vertices and the three interior angles."
},
{
"role": "assistant",
"conte... | geometry | triangles |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A angle-angle-side triangle has angles $167 {}^{\\circ}$ and $2 {}^{\\circ}$ and a side of length $5.5$. Determine the area, circumradius, inradius, and semiperimeter... | geometry | triangles |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A triangle has sides $11.56, 12.08, 2.23$. Determine the centroid, circumcenter, incenter, orthocenter, nine point center, and symmedian point of the triangle."
},
... | geometry | triangles |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A side-angle-side triangle has sides $10.14$ and $5.48$ and an angle $\\frac{17 \\pi }{180}$. Determine the centroid, circumcenter, incenter, orthocenter, nine point ... | geometry | triangles |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A triangle has sides $5, 4, 3$. Determine the locations of the triangle's vertices and the three interior angles."
},
{
"role": "assistant",
"content": "A... | geometry | triangles |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A triangle has sides $13., 6., 17.$. Determine points to define lines for the triangle's altitude, cevian, median, and symmedian lines."
},
{
"role": "assista... | geometry | triangles |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A angle-angle-side triangle has angles $166 {}^{\\circ}$ and $7 {}^{\\circ}$ and a side of length $5.5$. Determine the area, circumradius, inradius, and semiperimeter... | geometry | triangles |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A triangle has sides $\\frac{3}{2}, 8, \\frac{15}{2}$. Determine points to define lines for the triangle's altitude, cevian, median, and symmedian lines."
},
{
... | geometry | triangles |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A angle-side-angle triangle has angle $\\frac{\\pi }{12}$, a side of length $10.$ and an angle of measure $\\frac{11 \\pi }{180}$. Determine the centroid, circumcente... | geometry | triangles |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A triangle has sides $2.64, 3.06, 0.69$. Determine the locations of the triangle's vertices and the three interior angles."
},
{
"role": "assistant",
"con... | geometry | triangles |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A angle-side-angle triangle has angle $163 {}^{\\circ}$, a side of length $\\frac{27}{2}$ and an angle of measure $10 {}^{\\circ}$. Determine points to define lines f... | geometry | triangles |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A angle-angle-side triangle has angles $\\frac{163 \\pi }{180}$ and $\\frac{\\pi }{18}$ and a side of length $8.5$. Determine the locations of the triangle's vertices... | geometry | triangles |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A angle-side-angle triangle has angle $\\frac{29 \\pi }{180}$, a side of length $5.83$ and an angle of measure $\\frac{11 \\pi }{20}$. Determine the area, circumradiu... | geometry | triangles |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A triangle has sides $14, 9, 13$. Determine points to define lines for the triangle's altitude, cevian, median, and symmedian lines."
},
{
"role": "assistant"... | geometry | triangles |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A angle-side-angle triangle has angle $\\frac{\\pi }{5}$, a side of length $7$ and an angle of measure $\\frac{31 \\pi }{60}$. Determine points to define lines for th... | geometry | triangles |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A triangle has sides $5, 8, 8$. Determine the locations of the triangle's vertices and the three interior angles."
},
{
"role": "assistant",
"content": "A... | geometry | triangles |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A angle-angle-side triangle has angles $169 {}^{\\circ}$ and $8 {}^{\\circ}$ and a side of length $2.02$. Determine the centroid, circumcenter, incenter, orthocenter,... | geometry | triangles |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A triangle has sides $3.79, 5.62, 7.4$. Determine points to define lines for the triangle's altitude, cevian, median, and symmedian lines."
},
{
"role": "assi... | geometry | triangles |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A triangle has sides $4., 2.25, 5.5$. Determine points to define lines for the triangle's altitude, cevian, median, and symmedian lines."
},
{
"role": "assist... | geometry | triangles |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A angle-side-angle triangle has angle $38 {}^{\\circ}$, a side of length $11.75$ and an angle of measure $87 {}^{\\circ}$. Determine the locations of the triangle's v... | geometry | triangles |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A angle-side-angle triangle has angle $47 {}^{\\circ}$, a side of length $\\frac{9}{2}$ and an angle of measure $128 {}^{\\circ}$. Determine the area, circumradius, i... | geometry | triangles |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A angle-side-angle triangle has angle $95 {}^{\\circ}$, a side of length $\\frac{5}{2}$ and an angle of measure $69 {}^{\\circ}$. Determine the area, circumradius, in... | geometry | triangles |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A angle-angle-side triangle has angles $\\frac{37 \\pi }{45}$ and $\\frac{13 \\pi }{180}$ and a side of length $1.8$. Determine the area, circumradius, inradius, and ... | geometry | triangles |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A angle-side-angle triangle has angle $121 {}^{\\circ}$, a side of length $3.9$ and an angle of measure $22 {}^{\\circ}$. Determine points to define lines for the tri... | geometry | triangles |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A angle-side-angle triangle has angle $\\frac{\\pi }{3}$, a side of length $3.5$ and an angle of measure $\\frac{11 \\pi }{45}$. Determine the locations of the triang... | geometry | triangles |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A angle-angle-side triangle has angles $167 {}^{\\circ}$ and $6 {}^{\\circ}$ and a side of length $1.65$. Determine the centroid, circumcenter, incenter, orthocenter,... | geometry | triangles |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A side-angle-side triangle has sides $7.$ and $9.25$ and an angle $3 {}^{\\circ}$. Determine the area, circumradius, inradius, and semiperimeter of the triangle."
}... | geometry | triangles |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A side-angle-side triangle has sides $9$ and $5$ and an angle $\\frac{59 \\pi }{90}$. Determine the area, circumradius, inradius, and semiperimeter of the triangle."
... | geometry | triangles |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A triangle has sides $\\frac{11}{2}, \\frac{17}{2}, \\frac{11}{2}$. Determine the area, circumradius, inradius, and semiperimeter of the triangle."
},
{
"role... | geometry | triangles |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A angle-angle-side triangle has angles $8 {}^{\\circ}$ and $111 {}^{\\circ}$ and a side of length $\\frac{7}{2}$. Determine the centroid, circumcenter, incenter, orth... | geometry | triangles |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A angle-side-angle triangle has angle $33 {}^{\\circ}$, a side of length $10.8$ and an angle of measure $120 {}^{\\circ}$. Determine the area, circumradius, inradius,... | geometry | triangles |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A side-angle-side triangle has sides $12.55$ and $1.57$ and an angle $\\frac{17 \\pi }{90}$. Determine points to define lines for the triangle's altitude, cevian, med... | geometry | triangles |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A angle-side-angle triangle has angle $\\frac{29 \\pi }{30}$, a side of length $6.6$ and an angle of measure $\\frac{\\pi }{60}$. Determine the locations of the trian... | geometry | triangles |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A angle-side-angle triangle has angle $131 {}^{\\circ}$, a side of length $13.8$ and an angle of measure $37 {}^{\\circ}$. Determine the centroid, circumcenter, incen... | geometry | triangles |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A side-angle-side triangle has sides $4.1$ and $8.55$ and an angle $98 {}^{\\circ}$. Determine the centroid, circumcenter, incenter, orthocenter, nine point center, a... | geometry | triangles |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A triangle has sides $7., 1.5, 6.$. Determine points to define lines for the triangle's altitude, cevian, median, and symmedian lines."
},
{
"role": "assistan... | geometry | triangles |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A side-angle-side triangle has sides $2$ and $3$ and an angle $80 {}^{\\circ}$. Determine the centroid, circumcenter, incenter, orthocenter, nine point center, and sy... | geometry | triangles |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A triangle has sides $10.78, 8.9, 8.51$. Determine the area, circumradius, inradius, and semiperimeter of the triangle."
},
{
"role": "assistant",
"conten... | geometry | triangles |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A angle-side-angle triangle has angle $\\frac{13 \\pi }{15}$, a side of length $7$ and an angle of measure $\\frac{19 \\pi }{180}$. Determine the area, circumradius, ... | geometry | triangles |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A angle-angle-side triangle has angles $\\frac{41 \\pi }{45}$ and $\\frac{\\pi }{36}$ and a side of length $\\frac{9}{2}$. Determine points to define lines for the tr... | geometry | triangles |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A angle-angle-side triangle has angles $31 {}^{\\circ}$ and $3 {}^{\\circ}$ and a side of length $9.02$. Determine points to define lines for the triangle's altitude,... | geometry | triangles |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A side-angle-side triangle has sides $12$ and $7$ and an angle $\\frac{11 \\pi }{90}$. Determine points to define lines for the triangle's altitude, cevian, median, a... | geometry | triangles |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A side-angle-side triangle has sides $3.4$ and $6.4$ and an angle $\\frac{49 \\pi }{60}$. Determine points to define lines for the triangle's altitude, cevian, median... | geometry | triangles |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A triangle has sides $2., 2.75, 4.5$. Determine the locations of the triangle's vertices and the three interior angles."
},
{
"role": "assistant",
"conten... | geometry | triangles |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A triangle has sides $4.5, 9.5, 10.$. Determine the centroid, circumcenter, incenter, orthocenter, nine point center, and symmedian point of the triangle."
},
{
... | geometry | triangles |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A triangle has sides $2, 5, 6$. Determine the area, circumradius, inradius, and semiperimeter of the triangle."
},
{
"role": "assistant",
"content": "Semi... | geometry | triangles |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A triangle has sides $4., 9.5, 9.5$. Determine the locations of the triangle's vertices and the three interior angles."
},
{
"role": "assistant",
"content... | geometry | triangles |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A angle-angle-side triangle has angles $\\frac{67 \\pi }{90}$ and $\\frac{17 \\pi }{90}$ and a side of length $\\frac{5}{2}$. Determine points to define lines for the... | geometry | triangles |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A side-angle-side triangle has sides $10.25$ and $1.$ and an angle $\\frac{113 \\pi }{180}$. Determine the locations of the triangle's vertices and the three interior... | geometry | triangles |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A angle-angle-side triangle has angles $129 {}^{\\circ}$ and $15 {}^{\\circ}$ and a side of length $2.5$. Determine the centroid, circumcenter, incenter, orthocenter,... | geometry | triangles |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A angle-angle-side triangle has angles $68 {}^{\\circ}$ and $107 {}^{\\circ}$ and a side of length $7.$. Determine the locations of the triangle's vertices and the th... | geometry | triangles |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A angle-side-angle triangle has angle $\\frac{19 \\pi }{45}$, a side of length $13.75$ and an angle of measure $\\frac{\\pi }{2}$. Determine the locations of the tria... | geometry | triangles |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A side-angle-side triangle has sides $6.$ and $5.5$ and an angle $134 {}^{\\circ}$. Determine the centroid, circumcenter, incenter, orthocenter, nine point center, an... | geometry | triangles |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A triangle has sides $13., 11.5, 17.5$. Determine points to define lines for the triangle's altitude, cevian, median, and symmedian lines."
},
{
"role": "assi... | geometry | triangles |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A angle-side-angle triangle has angle $16 {}^{\\circ}$, a side of length $13$ and an angle of measure $148 {}^{\\circ}$. Determine the locations of the triangle's ver... | geometry | triangles |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A angle-angle-side triangle has angles $\\frac{17 \\pi }{20}$ and $\\frac{4 \\pi }{45}$ and a side of length $7$. Determine the centroid, circumcenter, incenter, orth... | geometry | triangles |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A angle-side-angle triangle has angle $\\frac{17 \\pi }{20}$, a side of length $5.25$ and an angle of measure $\\frac{4 \\pi }{45}$. Determine points to define lines ... | geometry | triangles |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A angle-side-angle triangle has angle $111 {}^{\\circ}$, a side of length $15.$ and an angle of measure $19 {}^{\\circ}$. Determine the area, circumradius, inradius, ... | geometry | triangles |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A side-angle-side triangle has sides $13.61$ and $1.83$ and an angle $\\frac{41 \\pi }{45}$. Determine the area, circumradius, inradius, and semiperimeter of the tria... | geometry | triangles |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A angle-angle-side triangle has angles $\\frac{5 \\pi }{9}$ and $\\frac{11 \\pi }{30}$ and a side of length $6.39$. Determine the centroid, circumcenter, incenter, or... | geometry | triangles |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A side-angle-side triangle has sides $5.$ and $7.5$ and an angle $\\frac{3 \\pi }{10}$. Determine the locations of the triangle's vertices and the three interior angl... | geometry | triangles |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A angle-side-angle triangle has angle $\\frac{29 \\pi }{90}$, a side of length $12.82$ and an angle of measure $\\frac{11 \\pi }{60}$. Determine the locations of the ... | geometry | triangles |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A triangle has sides $3.75, 0.75, 3.75$. Determine points to define lines for the triangle's altitude, cevian, median, and symmedian lines."
},
{
"role": "ass... | geometry | triangles |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A angle-side-angle triangle has angle $167 {}^{\\circ}$, a side of length $\\frac{21}{2}$ and an angle of measure $7 {}^{\\circ}$. Determine the centroid, circumcente... | geometry | triangles |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A angle-angle-side triangle has angles $82 {}^{\\circ}$ and $52 {}^{\\circ}$ and a side of length $9$. Determine the locations of the triangle's vertices and the thre... | geometry | triangles |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A triangle has sides $5.5, 7.5, 10.5$. Determine the centroid, circumcenter, incenter, orthocenter, nine point center, and symmedian point of the triangle."
},
{
... | geometry | triangles |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A angle-side-angle triangle has angle $\\frac{8 \\pi }{9}$, a side of length $4.96$ and an angle of measure $\\frac{7 \\pi }{180}$. Determine the centroid, circumcent... | geometry | triangles |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A angle-side-angle triangle has angle $69 {}^{\\circ}$, a side of length $5.5$ and an angle of measure $76 {}^{\\circ}$. Determine the centroid, circumcenter, incente... | geometry | triangles |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A triangle has sides $8, \\frac{25}{2}, 11$. Determine the centroid, circumcenter, incenter, orthocenter, nine point center, and symmedian point of the triangle."
}... | geometry | triangles |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A triangle has sides $2.5, 9.5, 10.5$. Determine the locations of the triangle's vertices and the three interior angles."
},
{
"role": "assistant",
"conte... | geometry | triangles |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A angle-side-angle triangle has angle $129 {}^{\\circ}$, a side of length $3.$ and an angle of measure $20 {}^{\\circ}$. Determine the locations of the triangle's ver... | geometry | triangles |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A triangle has sides $14., 1.75, 13.$. Determine the centroid, circumcenter, incenter, orthocenter, nine point center, and symmedian point of the triangle."
},
{
... | geometry | triangles |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A angle-angle-side triangle has angles $\\frac{37 \\pi }{180}$ and $\\frac{53 \\pi }{90}$ and a side of length $5$. Determine the locations of the triangle's vertices... | geometry | triangles |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A triangle has sides $8.27, 0.1, 8.28$. Determine the centroid, circumcenter, incenter, orthocenter, nine point center, and symmedian point of the triangle."
},
{... | geometry | triangles |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A triangle has sides $13, 6, \\frac{25}{2}$. Determine the locations of the triangle's vertices and the three interior angles."
},
{
"role": "assistant",
... | geometry | triangles |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A triangle has sides $13.33, 3.64, 15.4$. Determine the area, circumradius, inradius, and semiperimeter of the triangle."
},
{
"role": "assistant",
"conte... | geometry | triangles |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A angle-angle-side triangle has angles $93 {}^{\\circ}$ and $70 {}^{\\circ}$ and a side of length $7.75$. Determine the locations of the triangle's vertices and the t... | geometry | triangles |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A triangle has sides $\\frac{13}{2}, \\frac{23}{2}, 14$. Determine the locations of the triangle's vertices and the three interior angles."
},
{
"role": "assi... | geometry | triangles |
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