An airplane pilot over the Pacific sights an atoll at an angle of depression of 10°. At this time, the horizontal distance from the airplane to the atoll is 3,172 meters.

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03-05-2018
Mathematics

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An airplane pilot over the Pacific sights an atoll at an angle of depression of 10°. At this time, the horizontal distance from the airplane to the atoll is 3,172 meters.

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Edufirst Edufirst · Answer 1 · 2018-05-06T15:37:56+02:00

The question was posted incomplete.

This is the part missing:

What is the height of the plane to the nearest meter?

Answer: 559 m.

Explanation:

1) The horizontal distance between the plane and tha atoll makes a right triangle with the height, with the depression angle between the two legs.

2) Therefore, you can use the tangent trigonometric ratio:

tan(10°) = opposite-leg / adyacent-leg = height / horizontal distance

⇒ height = horizontal distance × tan (10°)

⇒ height = 3,172 m × tan(10°) = 559.31 m, which rounded to the nearest m is 559