A triangle has sides A, B, and C. Sides A and B are of lengths #1# and #2#, respectively, and the angle between A and B is #(2pi)/3 #. What is the length of side C?

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Answer 1 · 2018-03-17T11:40:19

#color(brown)(c = sqrt 7#

#a = 1, b = 2, hat C = (2pi) / 3#

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Applying Law of Cosine,

#c^2 = a^2 + b^2 - 2 a b sin C#

#c^2 = 1^2 + 2^2 - (2 * 1 * 2 * cos ((2pi)/3))#

#c^2 = 5 - 4 cos ((2pi)/3) = 5 + 4 cos (pi/3)# as #cos ((2pi)/3) = -cos (pi/3)# and cos is negative in II quadrant.

#c^2 = 5 + (4 * (1/2) ) = 5 + 2 = 7#

#color(brown)(c = sqrt 7#