Question

Amity wants to make a shade cloth for her back courtyard. The courtyard is in the shape of a triangle and the distances between the corner posts are shown on the diagram below.

What is the angle at each of the corners - A, B and C?
Give angles correct to the nearest minute.

Answer 1

To find the angles at each of the corners of the triangular courtyard, you can use the law of cosines. The law of cosines states that in any triangle, the square of one side is equal to the sum of the squares of the other two sides minus twice the product of the two sides multiplied by the cosine of the included angle.

Step-by-step explanation:

To find the angles at each of the corners of the triangular courtyard, we can use the law of cosines. The law of cosines states that in any triangle, the square of one side is equal to the sum of the squares of the other two sides minus twice the product of the two sides multiplied by the cosine of the included angle. In this case, we know the lengths of sides A, B, and C, so we can use the law of cosines to find the angles:

Step 1: Find the cosine of angle A: cos(A) = (B^2 + C^2 - A^2) / (2 * B * C)

Step 2: Find the cosine of angle B: cos(B) = (A^2 + C^2 - B^2) / (2 * A * C)

Step 3: Find the cosine of angle C: cos(C) = (A^2 + B^2 - C^2) / (2 * A * B)

Using these formulas, plug in the given lengths of sides A, B, and C and calculate the angles A, B, and C using a calculator or trigonometric tables.