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

Mar 20, 2016

Side c= 3 approx

#### Explanation:

Sides are given to be a=6, b=5 The angle between the two would be C. It is required to find side c. This can be done using cosine formula
cos C= $\frac{{a}^{2} + {b}^{2} - {c}^{2}}{2 a b}$. Plugging in the given values,

$\frac{\sqrt{3}}{2} = \frac{36 + 25 - {c}^{2}}{60}$

$30 \sqrt{3} = 61 - {c}^{2}$

${c}^{2} = 61 - 30 \sqrt{3}$= 61-51.96= 9 (approx)

c= 3