1982 AHSME Problems/Problem 18
In the adjoining figure of a rectangular solid, and . Find the cosine of .
WLOG, let .
Looking at square GHDC, we see that , which implies that and
Taking each cross-section one at a time, we look at square DHFB. We obviously know that CHB is a degree angle, giving , and .
Looking at square ABCD, we see that .
We now look at triangle DBH, which has side lengths , and . Because is opposite angle DHB, by the law of cosines,
Thus, the answer is