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Revision as of 22:45, 18 July 2016
Problem
A right prism with height 
has bases that are regular hexagons with sides of length 
. A vertex 
of the prism and its three adjacent vertices are the vertices of a triangular pyramid. The dihedral angle (the angle between the two planes) formed by the face of the pyramid that lies in a base of the prism and the face of the pyramid that does not contain measures 
degrees. Find 
.
Solution
Let 
and 
be the vertices adjacent to on the same base as , and let 
be the other vertex of the triangular pyramid. Then 
. Let 
be the foot of the altitude from to 
. Then since 
is a 
triangle, 
. Since the dihedral angle between 
and 
is 
, 
is a triangle and 
. Thus 
.
(Solution by gundraja)
See also
| 2016 AIME I (Problems • Answer Key • Resources) | ||
| Preceded by Problem 3 |
Followed by Problem 5 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
| All AIME Problems and Solutions | ||
These problems are copyrighted © by the Mathematical Association of America, as part of the American Mathematics Competitions. 
