If a plane is cruising at an altitude of 30,0000 feet wants to land at O'Hare, it must begin it's decent so that the angle of depression to the airport is 7 degrees. How many miles from the airport must the plane begin to descend?

The answer to your question is d = 3683.5 ft

Step-by-step explanation:

Data

Altitude = a = 30, Ф000 ft

angle = Ф = 7°

distance = d = ?

Process

To solve this problem we must use trigonometric functions. The trigonometric function that relates the Opposite side and the adjacent side is the tangent.

tan Ф = Opposite site / Adjacent side

-Solve for Opposite side (d)

Opposite side = Adjacent side x tan Ф

- Substitution

d = 30000 tan 7

-Simplification

d = 30000 (0.1228)

-Result

d = 3683.5 ft

-Conclusion

The plane must begin to descent 3683.5 ft before the airport.