Question

A plane is coming in for a landing on a runway that is 270m long as shown below. The planes angle of depression to the ends of the runway are 38 degrees and 44degreez respectively. Determine the height of the plane before it comes in for its landing.

Answer 1

304.6 metres

Explanation:

This is a trigonometry problem.

You know two angles and one side (a side that is not bounded by the two known angles).

Using the Sine Law,

A/Sine A = B/Sine B

Let A be the unknown length and B, the known length. Automatically, the angle corresponding to each side of the triangles is its angle.

The height of the plane - which is the side of the triangle that stretches from north to south - is what you are looking for. The angle facing this side directly is 44° (the angle at the left side of the base of this triangle). Same way side B (whose length is known) corresponds to angle 38° above it.

A = B (Sine A) ÷ Sine B

A = 270 (Sine 44°) ÷ Sine 38° = 270 (0.6947) ÷ 0.6157

A = 187.55776 ÷ 0.6157 = 304.625 ≅ 304.6 metres