A cat climbs onto a roof 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. What is the angle of depression in which the cat is looking down at you? Round to the nearest whole degree.
To find the angle of depression, we need to determine the horizontal distance between you and the cat.
We can use the Pythagorean theorem to calculate this distance. Let's call it x.
According to the theorem, the square of the hypotenuse (the diagonal distance) is equal to the sum of the squares of the other two sides (the horizontal and vertical distances).
Therefore, we have:
x^2 + 12^2 = 18^2
x^2 + 144 = 324
x^2 = 324 - 144
x^2 = 180
x = √180
x ≈ 13.42 feet
Now we can calculate the angle of depression by finding the arctan of the vertical distance (12 feet) divided by the horizontal distance (13.42 feet).
tan(angle) = 12/13.42
angle = arctan(12/13.42)
angle ≈ 41.3 degrees
Therefore, the angle of depression at which the cat is looking down at you is approximately 41 degrees.