Question

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

Answer 1

`|AC| = 2 sqrt{ 10 }`

Explanation:

The Law of the Cossins

`|AC|^2 = |AB|^2 + |BC|^2 - 2 * |AB| * |BC| * cos hat B`

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

`|AC| = sqrt{ 24 + 16 sqrt 2 * sqrt 2 / 2}`

`|AC| = sqrt{ 40 }`