# How do you find the exact value of the third side given triangle ABC, AB=2sqrt2, BC=4, mangleB=(3pi)/4?

Feb 13, 2017

#### Answer:

$| A C | = 2 \sqrt{10}$

#### Explanation:

The Law of the Cossins

$| A C {|}^{2} = | A B {|}^{2} + | B C {|}^{2} - 2 \cdot | A B | \cdot | B C | \cdot \cos \hat{B}$

|AC|^2 = 8 + 16 + 2 * 2 sqrt 2 * 4 * cos (180º - 135º)

$| A C | = \sqrt{24 + 16 \sqrt{2} \cdot \frac{\sqrt{2}}{2}}$

$| A C | = \sqrt{40}$