# A triangle has sides A, B, and C. Sides A and B are of lengths 4 and 7, respectively, and the angle between A and B is (2pi)/3 . What is the length of side C?

Nov 18, 2017

$C = \sqrt{93} \approx 9.64$

#### Explanation:

Using the Cosine Rule:

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

C^2=(7)^2+(4)^2-2(7)(4)cos((2pi)/3))

$\to {C}^{2} = 49 + 16 - \left(56 \cdot - \frac{1}{2}\right) = 93$

$C = \sqrt{93} \approx 9.64$