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1989 AIME Problems
10
10
Part of
1989 AIME Problems
Problems
(1)
Triangle Trig
Source:
2/21/2006
Let
a
a
a
,
b
b
b
,
c
c
c
be the three sides of a triangle, and let
α
\alpha
α
,
β
\beta
β
,
γ
\gamma
γ
, be the angles opposite them. If
a
2
+
b
2
=
1989
c
2
a^2+b^2=1989c^2
a
2
+
b
2
=
1989
c
2
, find
cot
γ
cot
α
+
cot
β
.
\frac{\cot \gamma}{\cot \alpha+\cot \beta}.
cot
α
+
cot
β
cot
γ
.
trigonometry
geometry
trig identities
Law of Cosines
Law of Sines