# A triangle has sides A, B, and C. Sides A and B are of lengths 8 and 9, respectively, and the angle between A and B is (pi)/8 . What is the length of side C?

Feb 29, 2016

c=3.4585

#### Explanation:

Given here are sides a =8 and b=9 and angle C=$\frac{\pi}{8}$ Apply cosine rule ti find out side c
Cos C= $\frac{{a}^{2} + {b}^{2} - {c}^{2}}{2 a b}$

$\cos \left(\frac{\pi}{8}\right) = \frac{64 + 81 - {c}^{2}}{144} = \frac{145 - {c}^{2}}{144}$

${c}^{2} = 145 - 144 \cos \left(\frac{\pi}{8}\right)$

$$     = 145-144(0.9238) =145-133.0386=11.9613


c= 3.4585