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Geometry and Trigonometry / Right triangles and trigonometry Difficulty: Medium
The figure presents triangle P Q R, where side P R is horizontal, and point Q is directly above point P. Angle P is a right angle. Angle R is labeled 30 degrees and side Q R is labeled 8.

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

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Explanation

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