Question

A traffic helicopter pilot 60 meters above the road spotted two antique cars. The angles of depression are 10.2 and 8.7 degrees. How far apart are the cars? A. 58.6 B. 392.1 C. 333.5 D. 57.8

Answer 1

58.6 is the answer to your question

Answer 2

Answer:

A. 58.6 meters

Step-by-step explanation:

Angle of depression denotes the angle when looking down from a certain height.

$tan10.2=\frac{60}{AD}\\\Rightarrow AD=\frac{60}{tan10.2}$

$tan 8.7=\frac{60}{AB}\\\Rightarrow AB=\frac{60}{tan8.7}$

DB = AB-AD

$\\\Rightarrow DB =\frac{60}{tan8.7}-\frac{60}{tan10.2}\\\Rightarrow DB = 392.1-333.47\\\Rightarrow DB = 58.63\ meters$

The cars are 58.6 meters apart.