Question

Elliott is standing at the top of a store escalator that leads to the ground floor below. The angle of depression from the top of the escalator to the floor is 36.84°, and the escalator is 15 feet long. How far is the top of the escalator from the ground floor? Round your answer to the nearest foot.

9 feet
12 feet
20 feet
36 feet

Answer 1

If I understand correctly, then the situation looks like this. In that case, cos(36.84) will be equal to the length of the adjacent leg (which is also the height of the elevator) divided by the hypotenuse (which is the length of the escalator, 15).
You may have heard "SOH CAH TOA", which is an easy way to remember this property of right triangles; Sin(a) is equal to the Opposite leg from angle a divided by Hypotenuse; Cos(a) is equal to the Adjacent leg from angle a divided by Hypotenuse; Tan(a) is equal to the Opposite leg from angle a divided by the Adjacent leg from angle a.
So, to find the height of the escalator, x, we can use the equation cos(36.84) = x/15; multiply both sides by 15 to get 15*cos(36.84) = x. From there, you can use a calculator to find your answer