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
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.