Question

A pilot flying at an altitude of 1.8km sights the runway directly in front of her. The angle of depression to the beginning of the runway is 31 degrees. The angle of depression to the end of the runway is 23 degrees. What is the length of the runway? Round to the nearest tenth of a kilometer.

Answer 1

Answer:

The answer is a

Step-by-step explanation:

The distance from the near end of the runway to the plane, divided by the altitude is the tangent of (90 degrees minus the angle of depression). Let "d1" be the distance to the near end of the runway, and "d2" be the distance to the far end of the runway. Let "a" be the altitude of the plane.

d1/a = tan(90 - 31)

d1 = a*tan(90 - 31)

d2/a = tan(90 - 23)

d2 = a*tan(90 - 23)

runway length = d2 - d1 = a*(tan(67) - tan(59))

length = 1800*(.6916) = 1245m = 1.2km

the answer is "a"

Answer 2

Length of runway = 1.2 km

See attached picture for solution: