1972 AHSME Problems/Problem 14
Problem
A triangle has angles of and . If the side opposite the angle has length , then the side opposite the angle has length
Solution
This triangle can be split into smaller 30-60-90 and 45-45-90 triangles. The side opposite the angle has length so the 30-60-90 triangle has sides and
One of the legs of the 45-45-90 triangles is so the hypotenuse is This is also the side opposite the angle, so the answer is
-edited by coolmath34
Solution 2
Use Law of Sines to get . The answer is .
-aopspandy