Question

A hot air balloon is flying at and altitude of 2101 feet. If the angle of depression from the pilot in the balloon to a house on the ground below is 31°, how far is the house from the pilot?

Answer 1

The problem is modelled as right angle triangle, shown in the diagram below

The distance between the pilot and the house is labelled as $x$

Using the trigonometry ratio of sine
$sin(31)= \frac{opposite}{hypotenuse}$
$sin(31)= \frac{2010}{x}$
$x= \frac{2101}{sin(31)} = 4079.3 ft$