Can someone help me with the question in this picture?
Thank you. :)

Question

Can someone help me with the question in this picture?
Thank you. :)

anonymous · Answer

attachment

anonymous · Answer

I have to find the variable.

zehanz · Answer

There are two variables, so that seems even harder to do, until you realize this is a 30-60-90 triangle, of which the sides have nice proportions: (see image)

zehanz · Answer

Think of it as half a equilateral triangle. 
The shortest side is exactly half the hypotenuse (longest side).
The longer side is $\sqrt{3}$ times the sortest side.

anonymous · Answer

Ahh okay. Thank you. So what do I do to find the variable?

zehanz · Answer

The longest side (hypotenuse) is 2√3. It is twice as long as the shortest side (=x), so now you know x.

zehanz · Answer

Once you've got x, multiply it with √3 to get y.

anonymous · Answer

So I would take x and multiply it by 2? Then multiply it with √3?

anonymous · Answer

Also, I'm not really sure how to find x. Do I do something with the numbers 60 and 30?

anonymous · Answer

$$\cos 60 = \frac{ x }{ 2 \sqrt 3 }$$ n cos 60 = 1/2

anonymous · Answer

$$\sin 60 = \frac{ y }{ 2 \sqrt 3 }$$ n sin 60 sqrt3/2

zehanz · Answer

x is the shortest side, it is half the longest, which is 2√3.
That is why x is √3.

y is x times √3, so it is √3 * √3 = 3.

anonymous · Answer

Ohh okay. Thank you.

zehanz · Answer

You really do not need sin or cos of angles here. It's all about the proportions of the sides. They are always a : a√3 : 2a (from shortest to longest)