1981 AHSME Problems/Problem 21
Problem 21
In a triangle with sides of lengths ,
, and
,
. The measure of the angle opposite the side length
is
Solution
First notice that exchanging for
in the original equation must also work. Therefore,
. Replacing
for
and expanding/simplifying in the original equation yields
, or
. Since
and
are positive,
. Therefore, we have an equilateral triangle and the angle opposite
is just 45^\circ\qquad\textbf{(D)}\.