Law of Cosines Calculator

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In a triangle ABC a,b,c are the sides. If the lengths of two sides ‘a’ and ‘b’ are given and the degree of angle

C is given, then according to the law of cosines the unknown side, c2 = a2 + b2 -2abcos(C). The online tool

used to evaluate using the Law of cosines is called as the Law of cosines calculator.



Example 1: Find the length of the side ‘c’ if the sides, a = 4, b = 6 and angle C=90°.


Given side length, a = 4 and b = 6 and angle C = 90°

According to the Law of Cosines: c2 = a2 + b2 -2abcos(C)

c2 = (4)2 + (6)2 + (2 * 4 * 6 * cos(90°))

c2 = 16 + 36 + (48 * 0)

c2 = 16 + 36 = 52 ->c = √52->c = 7.2

Hence the third side,c = 7.2



Example 2: Find the length of the side ‘a’ if the sides, b = 2, c = 3 and angle A=60°.


Given side length, b = 2 and c = 3 and angle A = 60°

According to the Law of Cosines: a2 = b2 + c2 -2bccos(A)

a2 = (2)2 + (3)2 + (2 * 2 * 3 * cos(60°))

a2 = 4 + 9 + (12 * 1/2)

a2 = 13 + 6 = 19->a = √19->a = 4.36

Hence the side,a = 4.36



 

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