A triangle has sides A, B, and C. Sides A and B are of lengths 2 and 3, respectively, and the angle between A and B is pi/12. What is the length of side C?

Apr 21, 2017

Third side is $1.187$

Explanation:

When two sides $a$ and $b$ and included angle $C$ between them is given, the third side is given by cosine formula i.e. ${c}^{2} = {a}^{2} + {b}^{2} - 2 a b \cos C$.

Here, we have $a = 2$ and $b = 3$ and C=pi/12=15°,

Hence, c^2=2^2+3^2-2×2×3×cos15°

= 4+9-12×0.966

= $13 - 11.592 = 1.408$

And $c = \sqrt{1.408} = 1.187$