# A triangle has sides A, B, and C. Sides A and B are of lengths 2 and 1, respectively, and the angle between A and B is (5pi)/12 . What is the length of side C?

Apr 9, 2018

color(blue)("As length of side c cannot be negative", color(brown)(c ~~ 2 " units"

#### Explanation:

$\text{Given : " a = 2, b = 1, hatC = (5pi)/12, " To find c}$

As per the Law of Cosines,

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

c = +- sqrt(2^2 + 1^2 - (2 * 2* 1 * cos ((5pi)/12))

$c = \pm \sqrt{5 - 4 \cos \left(\frac{5 \pi}{12}\right)} \approx 2 \text{ units}$

As length of side c cannot be negative, color(brown)(c ~~ 2 " units"