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Verizon [17]
2 years ago
9

Elliott is standing at the top of a store escalator that leads to the ground floor below. the angle of depression from the top o

f the escalator to the floor is 42.51°, and the escalator is 16 feet long. how far is the top of the escalator from the ground floor? round your answer to the nearest foot.
Mathematics
1 answer:
erma4kov [3.2K]2 years ago
4 0

By using what we know about right triangles, we conclude that the height is 11ft.

<h3>How far is the top of the escalator from the ground floor? </h3>

We can think of this as a right triangle.

Where the length of the escalator is the hypotenuse

We know that the angle of depression is 42.51°, then the top angle of our right triangle is:

90° - 42.51° = 47.49°

Now, the height of the top of the escalator would be the adjacent cathetus to said angle, then we can use the relation:

cos(a) = (adjacent cathetus)/(hypotenuse)

Replacing what we know:

cos(47.49°)  = height/16ft

cos(47.49°) *16ft = height = 10.8ft

Rounding to the nearest foot, we get:

height = 11ft

If you want to learn more about right triangles:

brainly.com/question/2217700

#SPJ1

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