2010 AMC 12B Problems/Problem 13
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Problem
In ,
and
. What is
?
Solution
We notice that the maximum values for the sine and the cosine function are both 1.
Therefore, the only way for this equation to be true is if and
, since if one of these equaled less than 1, the other one would have to be greater than 1 which contradicts our previous statement.
From this we easily conclude that
and
and solving this system gives us
and
. We can easily see that
is a
triangle with
,
, and