Question

Trigonometry

Answer 1

@extrinix

Answer 2

@dude @shadow

Answer 3

Oop tagged the senior mods…

Answer 4

You must use the \(SOH~CAH~TOA\) rule in order to solve this.

For the lower balloon, your side value is on the Hypotenuse compared to the angle. Meaning you must use \(cos\) in order to figure out what the length of the \(adjacent\) side is. The adjacent side is the side that you're using to figure out the difference between the height of the balloons.
\(Cos~(\theta)~=~\dfrac{Adjacent}{Hypotenuse}\)

Now, your adjacent is undefined, and your hypotenuse is defined (515m).
\(Cos~(15)~=~\dfrac{x}{515}\)

If you put that into your calculator, you will have the \(adjacent\) side for the lower balloon.

Answer 5

Now, in order to get the actual distance between each balloon, you need to find the \(adjacent\) side of the other balloon. Since we're looking for the adjacent side, and the Hypotenuse is defined, we will be using \(cos\) once again.
\(Cos~(\theta)~=~\dfrac{Adjacent}{Hypotenuse}\)

Our value for the hypotenuse is \(840m\) and our angle is \(22^o\).
\(Cos~(22)~=~\dfrac{x}{840}\)

Once you get that, you can then subtract the higher balloon's distance vertically from the person from the lower balloon's distance from the person.

Answer 6

And for reference if drawings make more sense to you: