Question

A traffic helicopter pilot 300 feet above the road spotted two antique cars. The angles of depression are 7.5° and 9º. How far apart are the cars? Round to the nearest tenth.

Answer 1

384.6 ft

Explanation:

The mnemonic SOH CAH TOA reminds you of the trig relation involving sides adjacent and opposite the angle. Here, the road distance is adjacent to the angle of depression, and the altitude is opposite. So, you have ...

Tan = Opposite/Adjacent

tan(7.5°) = (300 ft)/(distance to car 1)

tan(9°) = (300 ft)/(distance to car 2)

Solving for the distances, we have ...

distance to car 1 = (300 ft)/tan(7.5°) ≈ 2278.73 ft

distance to car 2 = (300 ft)/tan(9°) ≈ 1894.13 ft

Then the separation between the cars is ...

distance apart = 2278.73 ft - 1894.13 ft

distance apart = 384.6 ft