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)= (opposite)/(hypotenuse)`

`sin(31)= (2010)/(x)`

`x= (2101)/(sin(31)) = 4079.3 ft`