SAT Right triangles and trigonometry Practice Question 15 (Hard)

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Question bank / Right triangles and trigonometry

Math · Geometry and TrigonometryHard

In triangle $PQR$ , $PQ = PR = 10$ and $QR = 12$ . What is the value of $\cos Q$ ?

$\frac{4}{5}$

$\frac{3}{4}$

$\frac{4}{3}$

$\frac{3}{5}$

Show answer and explanation

Answer: D

Draw the altitude from $P$ to $\overline{QR}$ , meeting it at $M$ . Because the triangle is isosceles, $M$ is the midpoint of $\overline{QR}$ , so $QM = 6$ . In right triangle $PMQ$ , $\cos Q = \frac{QM}{PQ} = \frac{6}{10} = \frac{3}{5}$ .

Choice A is $\sin Q = \frac{PM}{PQ} = \frac{8}{10}$ , which uses the altitude instead of the adjacent side.

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