A pilot approaching a 3000-meter runway finds that the angles of depression of the ends of the runway are 14° and 20°. How far is the plane from the closer end of the runway? Round to the nearest tenth place.

Question

Mathematics

Liliana Mann

27 June, 13:18

A pilot approaching a 3000-meter runway finds that the angles of depression of the ends of the runway are 14° and 20°. How far is the plane from the closer end of the runway? Round to the nearest tenth place.

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Answers (1)

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Bryan Dean · Answer 1

Answer: The plane is 6,547 feet from the closer edge of the runway.

This is a trigonometry problem that will involve setting up 2 different triangles. One going to the closer edge of the runway and the other going to the far end of the runway.

The constant between the 2 triangles is the height of the plane. You can solve for this is both triangles and set them equal to each other.

Do that will give you the equation:

x/tan (70) = (x+3000) / tan (76) where x is the distance to the closer end of the runway.

If you solve that equation, you will get x = 6547 feet.