A triangle has sides A, B, and C. Sides A and B are of lengths #2# and #4#, respectively, and the angle between A and B is #pi/4#. What is the length of side C?

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Answer 1 · 2018-03-25T08:52:54

#color(indigo)("Length of side " c = sqrt (4 + 16 - (16/sqrt2)) ~~ 8.69 " Units"#

#Given : a = 2, b = 4, hat C = pi/4#

To find #"Length of side c"#

![https://in.pinterest.com/pin/548031848375604620/]( useruploads.socratic.org )

Applying Law of Cosines,

#c = sqrt(a^2 + b^2 - (2 a b cos C))#

#c = sqrt(2^2 + 4^2 - (2 * 2 * 4 * cos (pi/4)))#

#color(indigo)(c = sqrt (4 + 16 - (16/sqrt2)) ~~ 8.69#