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

Explanation:

Step1: Use the cosine function

The angle of depression is equal to the angle of elevation from the ground to the top of the escalator. Let the distance from the top of the escalator to the ground be \(x\). We know that \(\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}\). Here, \(\theta = 36.84^{\circ}\) and the hypotenuse (length of the escalator) \(c = 15\) feet.

$$x = 15\times\cos(36.84^{\circ})$$

Step2: Calculate the value

Using a calculator, \(\cos(36.84^{\circ})\approx0.8\)

$$x = 15\times0.8=12$$

Answer:

12 feet