Question

Select the correct answer.

A triangle has side lengths BC = 9, AB= 7, and AC = 13.
Which angle in the triangle has the greatest measure?

Answer 1

To find the angle with the greatest measure in a triangle, we can use the Law of Cosines. In this specific triangle, angle A has the largest measure.

Step-by-step explanation:

In a triangle, the side opposite the largest angle is the longest side. To determine which angle in the triangle has the greatest measure, we can use the Law of Cosines. According to the Law of Cosines, in a triangle with side lengths a, b, and c, the angle opposite the side with length c is given by:

cos(C) = (a^2 + b^2 - c^2) / (2ab)

Using this formula, we can find the angles of the triangle:

cos(A) = (BC^2 + AC^2 - AB^2) / (2 * BC * AC) = (9^2 + 13^2 - 7^2) / (2 * 9 * 13) = 0.3846
cos(B) = (AB^2 + AC^2 - BC^2) / (2 * AB * AC) = (7^2 + 13^2 - 9^2) / (2 * 7 * 13) = 0.9744
cos(C) = (AB^2 + BC^2 - AC^2) / (2 * AB * BC) = (7^2 + 9^2 - 13^2) / (2 * 7 * 9) = 0.641

The largest angle will have the smallest cosine value, so the angle with the greatest measure in this triangle is angle A.

Learn more about Triangle angles