<p><a href="http://tinypic.com/r/jku5ip/8">http://tinypic.com/r/jku5ip/8</a> </p>
<p>The answer is A</p>
<p>Can anyone please help me how to get the answer </p>
<p>that is a 30-60-90 triangle. Since we know that the 60 side is 4, we can find the 30 degree side by dividing by sqrt(3)., which gives you A. On a 30-60-90, the hypotenuse is 2<em>(length of 30 side) and 60 side is sqrt(3)</em>(length of 30 side)</p>
<p>Nowhere does the problem say that QS is a diameter of the circle, but if it is, then QRS is a 30-60-90 triangle.</p>
<p>Also, I got QR = 4 sqrt(3), not 4/sqrt(3), in which the answer would be D. Note that angle RQS is half of 60 deg, or 30 deg, so RS = 4 is the shorter leg of the 30-60-90 triangle.</p>
<p>Miter94 I got the same answer u got but in the answer key it says the answer is A !! I dont know how o.O</p>
<p>Guineagirl Can u tell me in details why did u divide by sqrt 3</p>
<p>@Omar186 What source is this problem from? I’ve done olympiad geometry and after reading the question several times, I don’t trust the answer key.</p>
<p>The measure of arc RS and ST are both 60 deg. This means that angles ROS and TOS are 60 deg, not RQS, TQS. After a bit of angle chasing, it follows that angle SQR = 60 deg, and RS = 4 is the shorter side of the right triangle.</p>
<p>@MITer94 you’re right, RS is the 30 deg side. I believe this is a mistake in the answer key also after taking a second look. There is a theorem that says an inscribed angle measures 1/2 its arc length, I made an incorrect assumption in my above post, which I guess the makers of the answer key did too.</p>
<p>(It’s been a while since I did geometry)</p>
<p>Thaanks @MITer94 and @guineagirl96 it’s from the princeton review manual for sat math level 1 </p>