A triangle has sides A, B, and C. Sides A and B are of lengths #11# and #4#, respectively, and the angle between A and B is #pi/6#. What is the length of side C?

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Answer 1 · 2018-03-25T06:50:23

#color(purple)(Length of side " c ~~ 14.06 " units"#

#a = 11, b = 4, hat C = pi/6#

To find length of side #c#.

Applying law of cosines,

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

#c^2 = 11^2 + 4^2 - (2 * 11 * 4 * cos (pi/6))#

#c^2 = 121 + 16 - (88 * sqrt3) / 2 = 197.79#

#color(purple)(Length of side " c ~~ 14.06 " units"#