Test 4 Section 3 Number 17

Above I’ve recreated the figure on the test, only my version adds labeled side lengths ab, and c. We’re told in the question that the sine of x° is 0.6. From SOH-CAH-TOA, we know that the sine of an angle is the ratio of its opposite side in a right triangle over the hypotenuse. In other words, \sin x^\circ =\frac{b}{c}=0.6.

We’re asked for the cosine of y°. Again, from SOH-CAH-TOA we know that the cosine of an angle is the ratio of its adjacent side in a right triangle over the hypotenuse. In this triangle, that means \cos y^\circ =\frac{b}{c}. Wait a minute…don’t we already know something about \frac{b}{c}? We sure do—that’s the same ratio as \sin x^\circ!

Therefore, we know that the cosine of y° is 0.6.