Question

Use the inverse of cosine to find the approximate interior angle measure at vertex B. Round your answer to the nearest tenth of a degree. Side AC of the right triangle is 8, Side AB of the right triangle is 17, Side CB of the right triangle is 15

Answer 1

First, we need to find the value of angle B using the Law of Cosines:

cos(B) = (a^2 + c^2 - b^2) / 2ac
cos(B) = (8^2 + 15^2 - 17^2) / (2 * 8 * 15)
cos(B) = (64 + 225 - 289) / 240
cos(B) = 0.1666666667

Now, we use the inverse cosine function to find the angle measure of B:

B = arccos(0.1666666667)
B ≈ 80.7 degrees

Therefore, the approximate interior angle measure at vertex B is 80.7 degrees.