1976 AHSME Problems/Problem 16
Let and let the altitude from to have length . This gives that . Since and are isosceles, we have that and . Since the sum of the inverse sine and cosine of any possible sine/cosine fraction is , we have that . Thus, and are supplementary, so is true while is not.
Applying the Pythagorean Theorem gives that the length of the altitude from to is and . This means that So we also have that is true while is not.
Thus, our answer is