# How do you solve a triangle if you are given A = 120 degrees, b = 3, c = 10?

Jun 21, 2018

color(brown)(c = sqrt139 = 11.79 " units"

#### Explanation:

hat A = 120, b = 3, c = 10, a = ?

Applying the Law of Cosines,

${a}^{2} = {b}^{2} + {c}^{2} - 2 b c \cos A$

${a}^{2} = {3}^{2} + {10}^{2} - \left(2 \cdot 3 \cdot 10 \cdot \cos \left(120\right)\right) = 139$

color(brown)(c = sqrt139 = 11.79 " units"