# How do you use the law of cosines to find BC given a triangle ABC with Angle A=123, BA=30 and CA=21?

Oct 7, 2016

$B C = 45.02$

#### Explanation:

Law of cosine : ${\left(B C\right)}^{2} = {\left(A B\right)}^{2} + {\left(A C\right)}^{2} - 2 \cdot \left(A B\right) \left(A C\right) \cos A$

$\implies {\left(B C\right)}^{2} = {30}^{2} + {21}^{2} - 2 \cdot 31 \cdot 21 \cdot \cos 123$

$\implies {\left(B C\right)}^{2} = 2874.03 \ldots .$
$\implies \left(B C\right) = \sqrt{2874.03}$
$\implies \left(B C\right) = 45.02 \ldots$