# A triangle has sides A, B, and C. Sides A and B are of lengths 1 and 2, respectively, and the angle between A and B is pi/4. What is the length of side C?

Feb 10, 2016

≈ 1.5

#### Explanation:

In this triangle , know 2 sides and the angle between them , so use 'cosine rule'

for this triangle the cosine rule is :

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

$= {1}^{2} + {2}^{2} - \left(2 \times 1 \times 2 \times \frac{1}{\sqrt{2}}\right)$

= 1 + 4 -  (4sqrt2)/2 = 5 - 2 sqrt2 ≈ 2.17

now C^2 ≈ 2.17 rArr C = sqrt2.17 ≈ 1.5