Question

Two runners in a marathon determine that the angles of elevation of a news helicopter are 39.5 degrees and 42 degrees. If the helicopter is 1950 feet directly above the finish line how far apart are the runners?

Answer 1

For a given angle of elevation θ, the distance from the runner to the finish lline is
.. d = 1950×cot(θ)

The difference in distance to the finish line is the distance between runners, so that distance is
.. d₁ -d₂ = 1950×(cot(θ₁) -cot(θ₂)
.. = 1950×(cot(39.5°) -cot(42°))
.. ≈ 200 . . . . feet

The runners are about 200 feet apart.