A cat climbs on top of a house and looks down at you. You are standing 12 feet away from the house and there is an 18-foot diagonal distance between you and the cat. Using the inverse of sine function, find the angle between the side of the house and the cat's line of sight looking down at you. Round your answer to the nearest whole degree.(1 point)
First, we need to find the distance between the cat and the house. Using the Pythagorean theorem, we can calculate this distance as:
distance = sqrt((diagonal distance)^2 - (distance from the house)^2)
distance = sqrt(18^2 - 12^2)
distance = sqrt(324 - 144)
distance = sqrt(180)
distance ≈ 13.42 feet
Next, we can find the angle between the side of the house and the cat's line of sight by using the inverse sine function:
angle = sin^(-1)(opposite/hypotenuse)
angle = sin^(-1)(12/13.42)
angle ≈ sin^(-1)(0.895)
angle ≈ 64.2 degrees
Therefore, the angle between the side of the house and the cat's line of sight looking down at you is approximately 64 degrees.