Difference between revisions of "1995 AIME Problems/Problem 12"
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== Problem == | == Problem == | ||
| + | Pyramid <math>\displaystyle OABCD</math> has square base <math>\displaystyle ABCD,</math> congruent edges <math>\displaystyle \overline{OA}, \overline{OB}, \overline{OC},</math> and <math>\displaystyle \overline{OD},</math> and <math>\displaystyle \angle AOB=45^\circ.</math> Let <math>\displaystyle \theta</math> be the measure of the dihedral angle formed by faces <math>\displaystyle OAB</math> and <math>\displaystyle OBC.</math> Given that <math>\displaystyle \cos \theta=m+\sqrt{n},</math> where <math>\displaystyle m_{}</math> and <math>\displaystyle n_{}</math> are integers, find <math>\displaystyle m+n.</math> | ||
== Solution == | == Solution == | ||
== See also == | == See also == | ||
| + | * [[1995_AIME_Problems/Problem_11|Previous Problem]] | ||
| + | * [[1995_AIME_Problems/Problem_13|Next Problem]] | ||
* [[1995 AIME Problems]] | * [[1995 AIME Problems]] | ||
Revision as of 01:28, 22 January 2007
Problem
Pyramid 
has square base 
congruent edges 
and 
and 
Let 
be the measure of the dihedral angle formed by faces 
and 
Given that 
where 
and 
are integers, find 
