A(1,-1) B(3,4) C(-3,3)
Measure the angle of A, B and C
sketch it on a graph
find the slopes
tangent of angle to +x axis = slope
If you mean to find the angles of triangle ABC, then find the lengths of sides a,b,c and use the law of cosines.
To measure the angle between three points A, B, and C on a coordinate plane, you can use the concept of trigonometry. Specifically, you can calculate the angles using the cosine rule.
1. Find the lengths of the three sides of the triangle formed by the three points A, B, and C. To find the length of a side, you can use the distance formula:
Length AB = √[(x2 - x1)^2 + (y2 - y1)^2]
Length BC = √[(x3 - x2)^2 + (y3 - y2)^2]
Length CA = √[(x1 - x3)^2 + (y1 - y3)^2]
For example, using the given points:
Length AB = √[(3 - 1)^2 + (4 - (-1))^2]
= √[2^2 + 5^2]
= √(4 + 25)
= √29
Similarly, calculate the lengths of BC and CA.
2. Now that you have the lengths of the three sides of the triangle, you can use the cosine rule to find the angle at each vertex.
Cosine rule:
cos(A) = (b^2 + c^2 - a^2) / (2 * b * c)
cos(B) = (a^2 + c^2 - b^2) / (2 * a * c)
cos(C) = (a^2 + b^2 - c^2) / (2 * a * b)
Where A, B, and C are the angles at vertices A, B, and C, respectively, and a, b, and c are the lengths of the opposite sides.
3. Plug in the calculated lengths of the sides into the cosine rule for each angle to obtain their cosine values.
Using the lengths calculated in step 1:
cos(A) = (√29^2 + √36^2 - √52^2) / (2 * √29 * √36)
cos(B) = (√52^2 + √9^2 - √29^2) / (2 * √52 * √9)
cos(C) = (√29^2 + √9^2 - √36^2) / (2 * √29 * √9)
4. Finally, use the inverse cosine function (cos⁻¹) to find the angle measure in degrees for each angle.
Angle A = cos⁻¹(cos(A))
Angle B = cos⁻¹(cos(B))
Angle C = cos⁻¹(cos(C))
Evaluate these expressions to get the angle measurements in degrees.