Question

A fighter pilot needs to make an emergency landing. He needs a clear space that is at least 600 m long to land safely. He is flying at an altitude of 300 m. He sees a small empty field. The angles of depression from the jet to the two ends of the field are 30° and 56° [5]
a) How long is the field?
b) Can he land safely?

Answer 1

(a) See the attached sketch. The jet makes a right triangle with the ground with hypotenuse y. Since the angle of depression is 56°, and the plane in which the jet is flying 300 m in the air is parallel with the ground, the angle of elevation in the right triangle is also 56°. Use the definition of sine to solve for y.

sin(56°) = (300 m)/y   →   y = (300 m)/sin(56°)

The uppermost angle in the blue triangle has measure equal to the difference between the two given angles of depression, 56° - 30° = 26°, and the rightmost angle is also 30° by the same reasoning as before. Then by the law of sines,

x/sin(26°) = y/sin(30°)   →   x = sin(26°)/sin(30°) y ≈ 317.2627 m

(b) No, the field is not long enough.