# How do you solve 7^2=11^2+9^2-2(11)(9)cosB?

Nov 26, 2016

$\angle B = {39.4}^{o}$

#### Explanation:

Simplifying each term in ${7}^{2} = {11}^{2} + {9}^{2} - 2 \left(11\right) \left(9\right) \cos B$

we get $49 = 121 + 81 - 198 \cos B$

or $49 = 202 - 198 \cos B$

or $198 \cos B = 202 - 49 = 153$

and $\cos B = \frac{153}{198} = 0.7727$

and using tables or scientific calculator

$\angle B = {\cos}^{- 1} 0.7727 = {39.4}^{o}$