# A triangle has sides A, B, and C. Sides A and B are of lengths 3 and 2, respectively, and the angle between A and B is pi/4. What is the length of side C?

Feb 9, 2016

$= 2.124$

#### Explanation:

Consider the diagram:

Use cosine rule:

color(orange)(C^2=A^2+B^2-(2ABcosc)

Here $A = 3 , B = 2$

Remember color(green)(pi=180^circ

$\rightarrow {C}^{2} = {3}^{2} + {2}^{2} - \left(2 \left(3\right) \left(2\right) \cos \left(\frac{\pi}{4}\right)\right)$

$\rightarrow {C}^{2} = 9 + 4 - \left(12 \cos {45}^{\circ}\right)$

$\rightarrow {C}^{2} = 13 - \left(12 \left(\frac{\sqrt{2}}{2}\right)\right)$

$\rightarrow {C}^{2} = 13 - \left(8.485 . .\right)$

$\rightarrow {C}^{2} = 4.515$

$\rightarrow C = \sqrt{4.515}$

color(blue)(C~~2.124..