A pilot can see the runway she is about to land on directly ahead. When looking at each end of the runway the angles of depression are 45 degrees and 42 degrees. If the airplane is 1500 ft off the ground, how long is the runway?

Question

Mathematics

Marlee Stephenson

18 October, 16:05

A pilot can see the runway she is about to land on directly ahead. When looking at each end of the runway the angles of depression are 45 degrees and 42 degrees. If the airplane is 1500 ft off the ground, how long is the runway?

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Answers (1)

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Kiersten Winters · Answer 1

We develop two different right triangles in which the opposite side to the given angle of depression is 1500 ft and the length of the runway is the y.

(45°) - - > tan (45°) = 1500 ft / y₁

y₁ = 1500 ft

(42⁰) - - > tan (42⁰) = 1500 ft / y₂

y₂ = 1665.92 ft

Finding the difference between two y's, the answer would be 165.92 ft.