An airplane is flying at an altitude of 10,000ft. The pilot wants to make a smooth final descent to the runway at a constant angle of depression of 4 degrees. How far from the runway should the pilot begin the descent?

The distance from the runway should be 143,267 ft

Step-by-step explanation: Please refer to the attached diagram for details.

If the pilot is flying at an altitude of 10,000 ft, his position would be point P, and the point G is the ground. Also the pilot wants to make a smooth descent to the runway which is point R. This means we have to calculate the distance from P to R (PR on the diagram).

Having derived a right angled triangle from the question, we can now write out the expression

Cos P = Adjacent/Hypotenuse

Cos 86 = 10000/PR

By cross multiplication we now have

PR = 10000/Cos 86

PR = 10000/0.0698

PR = 143, 266.4756

Approximately, distance PR = 143,267 ft

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