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 39.81°, and the escalator is 15.5 feet long. How far is the top of the escalator from the ground floor? Round your answer to the nearest foot. 19 feet 38 feet 10 feet 12 feet

Answer 1

The distance between the top of the escalator from the ground floor is:

12 feet

Explanation:

It is given that:

The angle of depression from the top of the escalator to the floor is 39.81°, and the escalator is 15.5 feet long.

We know that:

Now, we can model this problem with the help of a right angled triangle such that the side adjacent to 39.81° is x feet and the hypotenuse is 15.5 feet.

Hence, on using the cosine trignometric ratio we have:

`\cos 39.81\°=(adjacent)/(hypotenuse)\\\\i.e.\\\\\cos 39.81\°=(x)/(15.5)\\\\i.e.\\\\x=15.5* \cos 39.81\°}\\\\i.e.\\\\x=15.5* 0.7682\\\\i.e.\\\\x=11.9067\ feet`

which to the nearest feet is:

`x=12\ feet`

Answer 2

12ft

Explanation:

Behold, my crudely drawn diagram!!!

Edit: The red side is the hypotenuse/escalator length, the green side is adjacent to the angle/the escalator height, and the blue bits refer to the angle. Also it's supposed to be a right triangle but I forgot the little box we typically put in the corner to indicate the 90° angle.

Using some geometric knowledge of right triangles, we know that the Cosine of an angle is equal to the length of the adjacent side divided by the lenght of the hypotenuse. So:

Cos(39.81°) = h ÷ 15.5ft

*Here I've called the top of the escalator's height "h"*

By solving for h and plugging it into a calculator I get:

h = Cos(39.81°)•(15.5) = 11.906...

But they want it rounded to the nearest foot, so your answer is 12ft.