Question

Shane is 61 feet high on a ride at an amusement park. The angle of depression to the park entrance is 42°, and the angle of depression to his friends standing below is 80°. How far from the entrance are his

friends standing? Round to the nearest foot.

Answer 1

Let's call the distance from Shane to the entrance x and the distance from Shane to his friends y. We can use the tangent function to set up two equations:

tan(42) = 61 / x

tan(80) = 61 / y

Solving for y, we get:

y = 61 / tan(80)

y ≈ 12.2 feet

Therefore, Shane's friends are standing approximately 12.2 feet away from him.