A triangle has sides A, B, and C. Sides A and B are of lengths $3$ and $14$ , respectively, and the angle between A and B is $pi/6$ . What is the length of side C?

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Answer 1 · 2016-01-14T10:29:10

c ≅11.5

Law of cosines: $c^2 = a^2 + b^2 - 2ab cos Theta$
Where a and b are sides opposite angles A and B and $Theta$ is the included angle.

In this example $a=3, b=14 and Theta = pi/6$

Therefore: $c^2 = 3^2 + 14^2 - 2. 3.14 cos(pi/6)$
$c^2~= 9 + 196 - 84 * 0.8660254038$
$c ~= sqrt(132.25386608)$
$c ~= +- 11.5$ But c must be +ve

Therefore $c ~= 11.5$

A triangle has sides A, B, and C. Sides A and B are of lengths 33 and 1414, respectively, and the angle between A and B is pi/6pi/6. What is the length of side C?