Difference between revisions of "2003 AIME I Problems/Problem 11"
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== Problem == | == Problem == | ||
| + | An angle <math> x </math> is chosen at random from the interval <math> 0^\circ < x < 90^\circ. </math> Let <math> p </math> be the probability that the numbers <math> \sin^2 x, \cos^2 x, </math> and <math> \sin x \cos x </math> are not the lengths of the sides of a triangle. Given that <math> p = d/n, </math> where <math> d </math> is the number of degrees in <math> \arctan m </math> and <math> m </math> and <math> n </math> are positive integers with <math> m + n < 1000, </math> find <math> m + n. </math> | ||
== Solution == | == Solution == | ||
Revision as of 19:09, 6 August 2006
Problem
An angle 
is chosen at random from the interval 
Let 
be the probability that the numbers 
and 
are not the lengths of the sides of a triangle. Given that 
where 
is the number of degrees in 
and 
and 
are positive integers with 
find 
