OpenStudy (anonymous):

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

4 years ago
OpenStudy (anonymous):
4 years ago

OpenStudy (anonymous):

I have to find the variable.

4 years ago
OpenStudy (zehanz):

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)

4 years ago
OpenStudy (zehanz):

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.

4 years ago
OpenStudy (anonymous):

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

4 years ago
OpenStudy (zehanz):

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

4 years ago
OpenStudy (zehanz):

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

4 years ago
OpenStudy (anonymous):

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

4 years ago
OpenStudy (anonymous):

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

4 years ago
OpenStudy (anonymous):

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

4 years ago
OpenStudy (anonymous):

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

4 years ago
OpenStudy (zehanz):

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.

4 years ago
OpenStudy (anonymous):

Ohh okay. Thank you.

4 years ago
OpenStudy (zehanz):

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)

4 years ago