Question

A hot air balloon gets loose from its anchor the balloon operator is look at the balloon at an angle of inclination of 34. If the balloon is 50 feet in the air, what is the horizontal distance from the balloon to the balloon operator

Answer 1

horizontal distance = 74.13 ft

Explanation:

In order to solve this problem, we can start by drawing what the situation looks like. (see attached picture)

As we can see in the picture, we can build a right triangle with the balloon and the operator. We can use a trigonometric function so solve this. Specifically the tan function. We know that:

`tan \theta = (opposite)/(adjascent)`

in this case:

`tan \theta = (h)/(l)`

so we need to figure out what l is equal to. We can solve this equation for l, so we get:

`l=(h)/(tan \theta)`

and substitute the values given by the problem, so we get:

`l=(50ft)/(tan (30^(0)))`

which yields:

l=74.13 ft