SAT Right triangles and trigonometry Practice Question 7 (Medium)

Question bank / Right triangles and trigonometry

Math · Geometry and TrigonometryMedium

In right triangle $JKL$ , angle $K$ is the right angle. The cosine of angle $J$ is $0.6$ , and $JK = 9$ . What is the length of the hypotenuse $\overline{JL}$ ?

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Answer: 15

The cosine of angle $J$ is the adjacent side over the hypotenuse: $\cos J = \frac{JK}{JL}$ . So $0.6 = \frac{9}{JL}$ , which gives $JL = \frac{9}{0.6} = 15$ .

Multiplying instead of dividing gives $9 \times 0.6 = 5.4$ , which is shorter than a leg and can't be the hypotenuse.

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