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Law of Cosines
Toolkit 58
Law of Cosines
For a triangle with sides
a
a
a
,
b
b
b
,
c
c
c
:
a
2
=
b
2
+
c
2
−
2
b
c
cos
A
a^2=b^2+c^2-2bc\cos A
a
2
=
b
2
+
c
2
−
2
b
c
cos
A
or
cos
A
=
b
2
+
c
2
−
a
2
2
b
c
\cos A=\frac{b^2+c^2-a^2}{2bc}
cos
A
=
2
b
c
b
2
+
c
2
−
a
2
Related Problems
Core
AMC 12A 2024 (Problem 19)
AMC 12A 2022 (Problem 12)
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