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

Answer:

5668.3

Step-by-step 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:

$sin(34) = \frac{opposite}{hypotenuse}\\ \\sin(34) = \frac{altitude}{distance}\\\\sin(34) = \frac{2999}{distance}\\\\distance = \frac{2999}{sin34}\\\\distance = 5668.3 feet$

The pilot is 5668.3 feet far away from the house.