Question

The angle of depression from a helicopter to a landing pad is 37 degrees. if the helicopter is 1250 feet from the ground. what is the horizontal distance from the helicopter to the landing pad?

Answer 1

The horizontal distance from the helicopter to the landing pad is 1658.81 feet

Solution:

The figure is attached below

Triangle ABC is a rightangled triangle

A helicopter is flying at point A and landing pad is at point c

Angle of depression of the helicopter is 37 degrees so angle of elevation of this helicopter from landing pad will be same as 37 degrees

The helicopter is 1250 feet from the ground

Therefore, AB = 1250 feet

To find: horizontal distance from the helicopter to the landing pad

BC is the horizontal distance from the helicopter to the landing pad

BC = ?

By the definition of tan,

$tan \theta = \frac{opposite}{adjacent}$

$tan 37 = \frac{AB}{BC}\\\\tan 37 = \frac{1250}{BC}\\\\ 0.75355 = \frac{1250}{BC}\\\\BC = \frac{1250}{0.75355}\\\\BC = 1658.81$

Thus the horizontal distance from the helicopter to the landing pad is 1658.81 feet