30-60-90 triangle help?

Question

anonymous · Answer

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

I'm really uncertain of what to do here, so any guidance would be appreciated, thanks :)

anonymous · Answer

ok hang on

anonymous · Answer

Sure, no prob.

anonymous · Answer

answer or the equation?

anonymous · Answer

I have no idea what I'm doing, so whatever you can offer would be of great assistance lol.

anonymous · Answer

$$x:x \sqrt{3}:2x$$

anonymous · Answer

this is gonna be your equation that you will run off of ok first we know that the x is 18ft

anonymous · Answer

$$x \sqrt{3} =22ft$$

anonymous · Answer

and the 2x = 26 ft can you solve your gonna combine the terms

anonymous · Answer

$$x \sqrt{3}$$

Where does this come from though?

anonymous · Answer

sorry error this is your equation hang on and i will explain

anonymous · Answer

Alrighty

anonymous · Answer

$$18:18\sqrt{3}:26$$

anonymous · Answer

ok the rule to the 30:60:90 is $$x:x \sqrt{3}:2x$$

anonymous · Answer

that is the algebraic equation for the 30:60:90 triangle

anonymous · Answer

I think I'm gonna try this again tomorrow. I appreciate your willingness to help, and I'll go ahead and give you a medal. Thanks for everything :)

anonymous · Answer

fan me to please? i will help with other questions

anonymous · Answer

Sure :)

anonymous · Answer

thanks

hero · Answer

There's one good approach to 30-60-90 triangles that work.

anonymous · Answer

it is it works for me

hero · Answer

It takes more than just memorization to understand it.

hero · Answer

My approach is not the same as yours.

anonymous · Answer

can you explain it thats where my trouble came at i understand it but my problem was putting inthe numbers and what is your approach fan me please

hero · Answer

You start with the equilateral triangle, then you sort of divide it in half and derive the ratios.

anonymous · Answer

ok keep explaining it please

hero · Answer

|dw:1375580705534:dw|

You already know that an an equilateral triangle has three sides that are the same. But they also have the same angle 60°

hero · Answer

|dw:1375580818480:dw|

hero · Answer

Now, in this case, to make things more convenient, what you do is multiply each side by 2:|dw:1375580867590:dw|

hero · Answer

Then you split it in half:

|dw:1375580943762:dw|