Question

Isabell is standing at the top of a waterslide that leads to a pool below. The angle of depression from top of the slide to the pool is 20.81°, and the slide is 53 feet long. How far is the top of the slide from the ground? Round your answer to the nearest foot.

19 feet
42 feet
50 feet
139 feet

Answer 1

The top of the slide is 19 feet from the ground

Explanation:

The angle of depression is 20.81, hence the angle that the slide makes with its adjacent side (as in a right triangle) is 90 - 20.81 = 69.19°

Now, the slide is the hypotenuse, and we need to find the distance of the top to the ground. hence we need to find the length of the adjacent or vertical side.

So, we use SOHCAHTOA

In this case, CAH, to get,

cos(69.19) = A/(53)

A = 53(cos(69.19))

A = 18.83

A = 19 feet