SAT Right triangles and trigonometry Practice Question 13 (Hard)

Question bank / Right triangles and trigonometry

Math · Geometry and TrigonometryHard

Right triangles $ABC$ and $DEF$ are similar, with right angles at $B$ and $E$ , and vertex $A$ corresponds to vertex $D$ . If $\sin A = \frac{7}{25}$ and $DE = 48$ , what is the length of $\overline{EF}$ ?

$14$

$13.44$

$50$

$171.4$

Show answer and explanation

Answer: A

Because the triangles are similar, $\sin D = \sin A = \frac{7}{25}$ , so $\cos D = \frac{24}{25}$ (from the $7$ - $24$ - $25$ triangle). In triangle $DEF$ , $\overline{DE}$ is adjacent to angle $D$ , so $\cos D = \frac{48}{DF} = \frac{24}{25}$ , giving $DF = 50$ . Then $EF = DF \sin D = 50 \cdot \frac{7}{25} = 14$ .

Choice B multiplies $48$ by $\frac{7}{25}$ , treating leg $\overline{DE}$ as if it were the hypotenuse.

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