# A triangle has sides A, B, and C. Sides A and B are of lengths 7 and 2, respectively, and the angle between A and B is pi/6. What is the length of side C?

Apr 7, 2016

≈ 5.36 units

#### Explanation:

Given a triangle where we are given 2 sides and the angle between them. To find the 3rd side use the $\textcolor{b l u e}{\text{ cosine rule }}$

${c}^{2} = {a}^{2} + {b}^{2} - \left(2 a b \cos C\right)$

where a and b are the 2 known sides , C is the angle between them and c , the side to be found.

here a = 7 , b = 2 and C$= \frac{\pi}{6}$

now substitute these values into the $\textcolor{b l u e}{\text{ cosine rule }}$

 c^2 = 7^2 + 2^2 - (2xx7xx2xxcos(pi/6)

$= 49 + 4 - \left(28 \times \cos \left(\frac{\pi}{6}\right)\right) = 53 - \left(24.249\right) = 28.751$

now  c^2 = 28.751 rArr c = sqrt28.751 ≈ 5.36 " units "