# A triangle has sides A, B, and C. Sides A and B are of lengths 7 and 5, respectively, and the angle between A and B is pi/6. What is the length of side C?

Feb 5, 2016

C ≈ 3.66

#### Explanation:

Given a triangle with 2 sides and the angle between them known ,use the$\textcolor{b l u e}{\text{ cosine rule ")color(black)(" to solve for C}}$

In relation to this triangle the cosine rule is :

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

where $\theta \textcolor{b l a c k}{\text{ is the angle between A and B}}$

here A = 7 , B = 5 and $\theta = \frac{\pi}{6}$

$\Rightarrow {C}^{2} = {7}^{2} + {5}^{2} - \left[2 \times 7 \times 5 \times \cos \left(\frac{\pi}{6}\right)\right]$

= 49 + 25 - ( 60.6217..) ≈ 13,38

( remember this is${C}^{2}$)

rArr C = sqrt13.38 ≈ 3.66