Question

from the top of an apartment building, the angle of depression to a car parked on the street below is 38 degrees, as shown in the diagram below. the car is parked 80 feet from the base of the building. find the height of the building, to the nearest tenth of a foot.

Explanation:

Step1: Use the tangent function

The angle of depression is \(38^{\circ}\), and the adjacent side to the angle (distance from the base of the building to the car) is \(80\) feet. Let the height of the building be \(h\).
We know that \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\). Here, \(\theta = 38^{\circ}\), the opposite side is the height of the building \(h\), and the adjacent side \(a = 80\) feet.
So, \(\tan(38^{\circ})=\frac{h}{80}\).

Step2: Solve for \(h\)

We know that \(\tan(38^{\circ})\approx0.7813\).
From \(h = 80\times\tan(38^{\circ})\), substituting the value of \(\tan(38^{\circ})\), we get \(h=80\times0.7813 = 62.504\approx62.5\) feet.

Answer:

\(62.5\) feet