Question

Two airplanes leave the airport. Plane A departs at a 42° angle from the runway, and plane B departs at a 44° angle from the runway. Which plane has a larger horizontal distance from the airport when its altitude is 15 miles? Round the solutions to the nearest hundredth.

Plane B because it was 20.85 miles away
Plane A because it was 16.66 miles away
Plane A because it was 20.18 miles away
Plane B because it was 15.53 miles away

Answer 1

2nd choice

Explanation:

Horizontal distance = x

angle = α,

tanα = 15/x, so x = 15/tanα

For A, α = 42°, x = 15/tan42° = 16.66 miles

For B, α = 44°, x = 15/tan44° = 15.53 miles

so the answer is 2nd choice