¶ 1992 AIME Problem 7
Problem:
Faces and of tetrahedron meet at an angle of . The area of face is , the area of face is , and . Find the volume of the tetrahedron.
Solution:
Let be the foot of the perpendicular from to line . Since and the area of is . Next, let be the foot of the perpendicular from to plane . Then is a right triangle and measures . It follows that , and the volume of the tetrahedron is
The problems on this page are the property of the MAA's American Mathematics Competitions