Question

There are many ropes keeping a hot air balloon from floating away before a balloon race. One of these ropes is fixed to the ground at a 45° angle. Another is fixed to the ground at a 30° angle. If the hot air balloon is 15 feet off the ground, what is the distance between the ground directly underneath the balloon and the second rope rounded to the nearest hundredth of a foot? Type the numeric answer only in the box below.

Answer 1

Well I'm going to assume that the 30° angle is attached to the bottom of the balloon: so it creates a triangle like this:



We are solving for x

This is a 30 / 60 / 90 Triangle, which has sides:
\[1, \sqrt{3}, 2 \]

So the sides of that triangle are
\[15, \sqrt{45}, 30\]

Then x = \[\sqrt{45}\]