query stringlengths 22 409 | positive_passages listlengths 1 1 | negative_passages listlengths 20 20 | score float64 56 100 |
|---|---|---|---|
Query: How can I calculate the area when I only know the lengths of two sides and the angle between them? | [
{
"doc_id": 17476,
"text": "\\section{Area of Triangle in Terms of Two Sides and Angle} Tags: Triangles, Area of Triangle in Terms of Two Sides and Angle, Euclidean Geometry, Area Formulas, Areas of Triangles \\begin{theorem} The area of a triangle $ABC$ is given by: :$\\displaystyle \\frac 1 2 a b \\sin C... | [
{
"doc_id": 0,
"text": "['', 'A triangle has two sides, which measure 12cm and 14 cm, and the angle between them is 67 degrees. Find the area of the triangle using trigonometry.\\nTo find the area of the triangle, we can use the formula:\\n\\nArea = (1/2) * a * b * sin(C)\\n\\nwhere a and b are the lengths ... | 96 |
Query: If I have a triangle and measure two sides and the angle between them, what formula can I use to find the area? | [
{
"doc_id": 17476,
"text": "\\section{Area of Triangle in Terms of Two Sides and Angle} Tags: Triangles, Area of Triangle in Terms of Two Sides and Angle, Euclidean Geometry, Area Formulas, Areas of Triangles \\begin{theorem} The area of a triangle $ABC$ is given by: :$\\displaystyle \\frac 1 2 a b \\sin C... | [
{
"doc_id": 0,
"text": "['', 'A triangle has two sides, which measure 12cm and 14 cm, and the angle between them is 67 degrees. Find the area of the triangle using trigonometry.\\nTo find the area of the triangle, we can use the formula:\\n\\nArea = (1/2) * a * b * sin(C)\\n\\nwhere a and b are the lengths ... | 96 |
Query: What is the formula for finding the area of a triangle if you only have the lengths of two sides and the included angle? | [
{
"doc_id": 17476,
"text": "\\section{Area of Triangle in Terms of Two Sides and Angle} Tags: Triangles, Area of Triangle in Terms of Two Sides and Angle, Euclidean Geometry, Area Formulas, Areas of Triangles \\begin{theorem} The area of a triangle $ABC$ is given by: :$\\displaystyle \\frac 1 2 a b \\sin C... | [
{
"doc_id": 0,
"text": "['', 'A triangle has two sides of length 10 units and 15 units, with a included angle of 60 degrees. What is the area of the triangle?\\nTo find the area of the triangle, we can use the formula for the area of a triangle when two sides and the included angle are given:\\n\\nArea = (1... | 96 |
Query: Imagine I'm building a triangular garden bed and I've measured two sides and the angle between them, how do I figure out its area? | [
{
"doc_id": 17476,
"text": "\\section{Area of Triangle in Terms of Two Sides and Angle} Tags: Triangles, Area of Triangle in Terms of Two Sides and Angle, Euclidean Geometry, Area Formulas, Areas of Triangles \\begin{theorem} The area of a triangle $ABC$ is given by: :$\\displaystyle \\frac 1 2 a b \\sin C... | [
{
"doc_id": 0,
"text": "['', 'A triangle has two sides, which measure 12cm and 14 cm, and the angle between them is 67 degrees. Find the area of the triangle using trigonometry.\\nTo find the area of the triangle, we can use the formula:\\n\\nArea = (1/2) * a * b * sin(C)\\n\\nwhere a and b are the lengths ... | 96 |
Query: When the sides of a triangle are 5m and 7m, and the included angle is 60 degrees, how do I find the area? | [
{
"doc_id": 17476,
"text": "\\section{Area of Triangle in Terms of Two Sides and Angle} Tags: Triangles, Area of Triangle in Terms of Two Sides and Angle, Euclidean Geometry, Area Formulas, Areas of Triangles \\begin{theorem} The area of a triangle $ABC$ is given by: :$\\displaystyle \\frac 1 2 a b \\sin C... | [
{
"doc_id": 0,
"text": "['', 'A triangle has two sides of length 10 units and 15 units, with a included angle of 60 degrees. What is the area of the triangle?\\nTo find the area of the triangle, we can use the formula for the area of a triangle when two sides and the included angle are given:\\n\\nArea = (1... | 96 |
Query: How can I calculate the area of a triangle if I only know two sides and the angle between them? | [
{
"doc_id": 17476,
"text": "\\section{Area of Triangle in Terms of Two Sides and Angle} Tags: Triangles, Area of Triangle in Terms of Two Sides and Angle, Euclidean Geometry, Area Formulas, Areas of Triangles \\begin{theorem} The area of a triangle $ABC$ is given by: :$\\displaystyle \\frac 1 2 a b \\sin C... | [
{
"doc_id": 0,
"text": "['', 'A triangle has two sides, which measure 12cm and 14 cm, and the angle between them is 67 degrees. Find the area of the triangle using trigonometry.\\nTo find the area of the triangle, we can use the formula:\\n\\nArea = (1/2) * a * b * sin(C)\\n\\nwhere a and b are the lengths ... | 96 |
Query: I'm trying to figure out the formula for finding the area of a triangle when given two side lengths and the included angle. Can you help? | [
{
"doc_id": 17476,
"text": "\\section{Area of Triangle in Terms of Two Sides and Angle} Tags: Triangles, Area of Triangle in Terms of Two Sides and Angle, Euclidean Geometry, Area Formulas, Areas of Triangles \\begin{theorem} The area of a triangle $ABC$ is given by: :$\\displaystyle \\frac 1 2 a b \\sin C... | [
{
"doc_id": 0,
"text": "['', 'A triangle has two sides of length 10 units and 15 units, with a included angle of 60 degrees. What is the area of the triangle?\\nTo find the area of the triangle, we can use the formula for the area of a triangle when two sides and the included angle are given:\\n\\nArea = (1... | 96 |
Query: If I have a triangular garden bed and want to plant flowers in it, how much space will I have if I know two sides and the angle between them? | [
{
"doc_id": 17476,
"text": "\\section{Area of Triangle in Terms of Two Sides and Angle} Tags: Triangles, Area of Triangle in Terms of Two Sides and Angle, Euclidean Geometry, Area Formulas, Areas of Triangles \\begin{theorem} The area of a triangle $ABC$ is given by: :$\\displaystyle \\frac 1 2 a b \\sin C... | [
{
"doc_id": 0,
"text": "['', \"In a garden, there are yellow and green flowers which are straight and curved. If the probability of picking a green flower is 2/3 and picking a straight flower is 1/2, then what is the probability of picking a flower which is yellow and straight\\nAnswer Choices: (A) 1/6 (B) ... | 96 |
"Query: Could you explain why the area of a triangle is calculated as half the product of two sides (...TRUNCATED) | [{"doc_id":17476,"text":"\\section{Area of Triangle in Terms of Two Sides and Angle} Tags: Triangles(...TRUNCATED) | [{"doc_id":0,"text":"['', 'A triangle has two sides of length 10 units and 15 units, with a included(...TRUNCATED) | 96 |
Query: What if the angle between the two sides is obtuse? | [{"doc_id":17476,"text":"\\section{Area of Triangle in Terms of Two Sides and Angle} Tags: Triangles(...TRUNCATED) | [{"doc_id":0,"text":"['', \"\\\\begin{definition}[Definition:Obtuse Angle]\\nAn '''obtuse angle''' i(...TRUNCATED) | 88 |
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