Law of Cosines
One side of a triangle when opposite angle and two sides are known
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The "Law of Cosines" can be used to calculate one side of a triangle when the angle opposite and the other two sides are known.
The "Law of Cosines" can be expressed as
c2 = a2 + b2 - 2 a b cos C (1)
where
a, b and c = length of triangle sides (m, ft ..)
C = angle opposite side c (degrees)
Example - Calculate Side in Triangle
If side a = 1 m, side b = 1.3 m and angle C = 60 degrees - the side c can be calculated by modifying 1 to
c = ((1 m)2 + (1.3 m)2 - 2 (1 m ) (1.3 m) cos(60 degrees))1/2
= 1.18 m
Law of Cosines Calculator
The generic calculator below can used to calculate the side c:
Law of Cosines - Excel Template
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