In the right triangle shown above, what is the length of ?

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Accepted Answer

The correct answer is 4. Triangle PQR has given angle measures of 30&deg; and 90&deg;, so the third angle must be 60&deg; because the measures of the angles of a triangle sum to 180&deg;. For any special right triangle with angles measuring 30&deg;, 60&deg;, and 90&deg;, the length of the hypotenuse (the side opposite the right angle) is 2 x , where x is the length of the side opposite the 30&deg; angle. Segment PQ is opposite the 30&deg; angle. Therefore, 2( PQ ) = 8 and PQ = 4.

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