# How do you use the law of cosines if you are given three sides 9, 6, 14?

Jul 4, 2015

Solve triangle knowing the 3 sides.

#### Explanation:

Use trig identity: c^2 = a^2 + b^2 - 2abcos C. Find angles A, B, and C

196 = 81 + 36 - 108cos C
108cos C = 117 - 196 = -79 ->$\cos C = - \frac{79}{108} = - 0.73$
->$C = 137$ deg
$\sin \frac{B}{b} = \sin \frac{C}{c} \to \sin B = \frac{b \sin C}{c} = \frac{6 \left(0.68\right)}{14} = 0.29$
-->$B = 16.94$

$A = 180 - B - C = 180 - 137 - 16.94 = 26.06$