How to solve this special triangle?

Question

anonymous · Answer

attachment

anonymous · Answer

law of cosine

zepdrix · Answer

In a 30/60/90 triangle,

the shortest leg is half the length of the longest leg, see how they gave that to us?

zepdrix · Answer

Then the medium length leg is sqrt(3) times the shortest leg.

anonymous · Answer

but how do find x, this is so confusing

zepdrix · Answer

x is the length of the medium leg.

zepdrix · Answer

Since this is a special triangle, just try to remember the rule.

Do you know how to identify which side is the `hypotenuse`?

anonymous · Answer

the hypotenuse is the longest side and across from 90

zepdrix · Answer

Across from the 90? Ok good!
So our hypotenuse is 12.

The `shortest leg` has a length of half of the hypotenuse.
See how they labeled it for us?

6 is half of 12.

zepdrix · Answer

The `medium leg`, which is labeled as x, will have a length of `shortest leg` times sqrt(3).

zepdrix · Answer

Take your shortest leg, multiply it by $\Large\bf\sf \sqrt{3}$ and that will be the length of the side x.

anonymous · Answer

okay give me a sec

anonymous · Answer

i got 10.4

zepdrix · Answer

Ok good job!
Your teacher might want you to leave it in radical form which would be $\Large\bf\sf 6\sqrt{3}$.

But ya 10.4 is a good approximation.
The instructions didn't specify either way, so whatever is fine :)

anonymous · Answer

thank you so much

zepdrix · Answer

np \c:/