+0

# Math World Problem #3

0
118
1
+124

Charles lives in a tall apartment building. He looks out his window and spots a car on the road that runs straight toward his building. His angle of depression to the car is 24°.

Charles looks farther down the road and spots a dump truck. He estimates that the car is 800 feet in front of the dump truck. His angle of depression to the dump truck is 10°.

How far above the ground is Charles's line of sight?

Feb 22, 2020

$$\text{let the distance to the truck be L}\\ h = L \tan(10^\circ)\\ h = (L-800)\tan(24^\circ)\\ (L-800)\tan(24^\circ)=L \tan(10^\circ)\\ L = \dfrac{800 \tan(24^\circ)}{\tan(24^\circ)-\tan(10^\circ)}\\ h = \dfrac{800 \tan(24^\circ)}{\tan(24^\circ)-\tan(10^\circ)}\tan(10^\circ)$$