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.

Question

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.

Answer 1

First, we need to find the height of the house that the cat is on. We can use the Pythagorean theorem to do this.

Let h be the height of the house. The distance from you to the house is 12 feet, and the diagonal distance from you to the cat is 18 feet. Using the Pythagorean theorem:

h^2 + 12^2 = 18^2
h^2 + 144 = 324
h^2 = 180
h = √180
h ≈ 13.42 feet

Now, we can find the angle between the side of the house and the cat's line of sight looking down at you using the inverse sine function. Let θ be the angle we are looking for.

sin(θ) = opposite/hypotenuse
sin(θ) = 13.42/18
sin(θ) ≈ 0.7456

Now, we can use the inverse sine function to find the angle θ.

θ = sin^(-1)(0.7456)
θ ≈ 48.82 degrees

Rounded to the nearest whole degree, the angle between the side of the house and the cat's line of sight looking down at you is approximately 49 degrees.