Test 4 Section 3 Number 17

Above I’ve recreated the figure on the test, only my version adds labeled side lengths *a*, *b*, 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, .

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 . Wait a minute…don’t we already know something about ? We sure do—that’s the same ratio as !

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