A cat climbs onto a roof and looks down at you. You are standing 12 feet away from the house and there is a 18-foot diagonal between you and the cat. What is the angle of depression from the cat to you? Round your answer to the nearest whole number.
To find the angle of depression from the cat to you, we can use the tangent function.
Tangent(angle) = opposite/adjacent
In this case, the opposite side length is 12 feet (the distance from you to the house) and the adjacent side length is 18 feet (the diagonal distance between you and the cat).
So, tan(angle) = 12/18
tan(angle) = 2/3
Taking the inverse tangent of both sides to solve for the angle:
angle = tan^(-1)(2/3)
angle ≈ 33 degrees
Therefore, the angle of depression from the cat to you is approximately 33 degrees.