Question

A​ hot-air balloon is flying at an altitude of 2999 feet. If the angle of depression from the pilot in the balloon to a house on the ground below is 34degrees​, how far is the house from the​ pilot?

Answer 1

5668.3

Explanation:

The problem can be represented as a right angled triangle as shown below.

The angle of depression is equivalent to the angle inside the triangle (alternate angles) and it is 34°.

The altitude of the balloon is 2999 feet. (opposite)

Using trigonometric function, SOHCAHTOA, we can solve this:

`sin(34) = (opposite)/(hypotenuse)\\ \\sin(34) = (altitude)/(distance)\\\\sin(34) = (2999)/(distance)\\\\distance = (2999)/(sin34)\\\\distance = 5668.3 feet`

The pilot is 5668.3 feet far away from the house.