Question

A plane is flying at an altitude of 25,000 m. From the pilot, the angle of depression to the airport tower is 30°. How far is the tower from a point directly beneath the plane? Round your answer to the nearest tenth.

Answer 1

The question is modelled as shown in the diagram below

We have the angle, 30° and we know the length of the side opposite the angles, 25000 feet. We are looking for the ground distance between the plane and the tower. We will use the trigonometry ratio of Tan

$tan(x)= \frac{opposite}{adjacent}$
$tan(30)= \frac{25000}{y}$
$y= \frac{25000}{tan(30)}$
$y=43301.27019$

The distance between the point directly beneath the plane and the tower is 43301.3 feet (rounded to  2dp)