# Finding two sides of a triangle [duplicate]

Possible Duplicate:
calculate sides of the right triangle if I know 1 side and all the angles

I'm not sure how to do this with only 1 side given, but I have a right triangle with a 30 degree angle and an unmarked angle. One side is 4 and the other two are x any y.

How do I find the values of x and y?

I think the hypotenuse is x adjacent is y and 4 is opposite.

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## marked as duplicate by Willie WongJun 6 '11 at 12:13

Do you know how the sine and cosine of an angle are related to a right triangle? Maybe this will be helpful: en.wikipedia.org/wiki/… – Apostolos Jun 5 '11 at 23:51
I know of that but not how to apply it. – Adam Jun 5 '11 at 23:52
Hint: apply the definition of sine and cosine (geometrically, what do they mean?) – soandos Jun 5 '11 at 23:53
Possible Duplicate: math.stackexchange.com/q/12352/9003 First of all, you should be able to calculate the third angle: it's a right triangle, whose angles add up to 180, and you know it has a 90 degree angle, and a 30 degree angle, so "unmarked" angle is 180 - 90 - 30 = unmarked angle. Now, please see the question I've linked you to, which addresses the very same problem. – amWhy Jun 5 '11 at 23:53
Since $sin(30^\circ)=\frac{1}{2}$, $cos(30^\circ)=\frac{\sqrt{3}}{2}$ and $\tan(30^\circ)=\sqrt{3}$, if for example the hypotenuse is the side given then you have that the side opposite (O) to the 30 degree angle is $\frac{O}{7}=sin(30^\circ)$ which gives you $O=7\cdot\frac{1}{2}$. If the side given is not the hypotenuse solve a similar equation accordingly – Apostolos Jun 6 '11 at 0:00

Well, it's a right triangle. So one angle is 90, one is 30, and the other makes the sum be 180. So we know that angle.

Further, it matters which side is 7. Is it the hypotenuse? Is it a leg?

Finally, a right triangle with an angle of 30 has some very nice properties - it's well-studied, just like the 45-45-90 triangle. Do you know them?

I will not, unfortunately, tell you the answer as this is a homework question (but I appreciate you marking that - in the future, add other tags that mention what the question is actually about. I will edit your tags appropriately here).

Please comment on your work, and I'll guide you through the rest.

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I've flagged the question as an exact duplicate, where there are 4 answers; but +1 for not solving the problem for him... – amWhy Jun 6 '11 at 0:00
@amWhy: Incidentally, I flagged it too. ;p – mixedmath Jun 6 '11 at 0:01
I am not certain but the 4 (meant 4 not 7) the opposite I believe. – Adam Jun 6 '11 at 0:06
@mixedmath: great minds think alike! :D – amWhy Jun 6 '11 at 0:08
So I think that 4/x = sin – Adam Jun 6 '11 at 0:25