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 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.Group of answer choices41 feet17 feet12 feet11 feet
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 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.Group of answer choices41 feet17 feet12 feet11 feet
Solution
To solve this problem, we can use the concept of trigonometry. Specifically, we can use the cosine of the angle of depression. The cosine of an angle in a right triangle is equal to the adjacent side (which in this case is the distance from the top of the escalator to the ground floor) divided by the hypotenuse (which is the length of the escalator).
The formula is:
cos(angle) = adjacent/hypotenuse
We can rearrange this formula to solve for the adjacent side (the distance from the top of the escalator to the ground floor):
adjacent = cos(angle) * hypotenuse
Substituting the given values:
adjacent = cos(42.51°) * 16 feet
Using a calculator to find the cosine of 42.51° and then multiplying by 16, we get approximately 12 feet.
So, the top of the escalator is about 12 feet from the ground floor.
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