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? Type the numeric answer only in the box below.

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? Type the numeric answer only in the box below.

anonymous · Answer

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anonymous · Answer

Ooooh, this involves a 45-45-90 triangle AND a 30-60-90 triangle!

So in order to find the distance between the two ropes on the ground, we're going to have to find the distance x and another distance which I will call y. Here's a diagram to show you what I mean.
|dw:1346877448214:dw|

anonymous · Answer

ok i see

anonymous · Answer

OK, so following the 45-45-90 triangle rule, distance y is 18. Following the 30-60-90 rule, distance x is $$18\sqrt{3}$$

anonymous · Answer

The answer in numerical form is 13.18 feet.