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 18 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?

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 18 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?

anonymous · Answer

So the problem is only about the 30 degree rope, right?  

The rope, the height, and the ground make a 30-60-90 triangle.  The height is across from the 30 degree angle, so it must be the shortest side.

The rule for 30-60-90 triangles is short :: medium :: long = x :: x(root3) :: 2x.  For example, if the short side is 4, the medium side is 4(root 3) and the long side is 2*4=8.

So, the short side is 6 in this case.  How long must the medium side be?