1982 AHSME Problems/Problem 23
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Contents
Problem
The lengths of the sides of a triangle are consecutive integers, and the largest angle is twice the smallest angle. The cosine of the smallest angle is
Solution 1
In let
and
for some positive integer
We are given that
and we need
We apply the Law of Cosines to solve for
We apply the Law of Cosines to solve for
By the Double-Angle Formula
we have
from which
Recall that
is a positive integer, so
By substitution, the answer is
~MRENTHUSIASM
Solution 2
See Also
1982 AHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 22 |
Followed by Problem 24 | |
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