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.

Answer 1

Check the picture below.

make sure your calculator is in Degree mode.

Answer 2

9 ft.

Explanation:

Let h represent the distance between top of the escalator from the ground floor.

We have been given that the angle of depression from the top of the escalator to the floor is 36.84°, and the escalator is 15 feet long.

We can see from our attachment that the angle of depression, escalator and h forms a right triangle with respect to ground. The side h is opposite side and 15 feet side is hypotenuse of right triangle.

`\text{sin}=\frac{\text{Opposite}}{\text{Hypotenuse}}`

`\text{sin}(36.84^(\circ))=(h)/(15)`

`\text{sin}(36.84^(\circ))*15=(h)/(15)*15`

`0.599582468446*15=h`

`8.993737=h`

`h\approx 9`

Therefore, the top of the escalator is 9 feet far from the ground floor.