# How do you find the exact value of the third side given triangle ABC, b=4, c=4, and mangleA=pi/3?

Feb 7, 2017

Applying the Cosine Rule , ${a}^{2} = {b}^{2} + {c}^{2} - 2 b c \cos A$

$= 16 + 16 - 2 \left(4\right) \left(4\right) \cos \left(\frac{\pi}{3}\right) = 16 + 16 - 2 \left(4\right) \left(4\right) \left(\frac{1}{2}\right)$

$= 16 + 16 - 16 = 16$.

$\therefore a = 4$.

Alternatively , in DeltaABC, b=c rArr m/_B=m/_C, &, m/_A=pi/3

$\Rightarrow m \angle B = m \angle C = m \angle A = \frac{\pi}{3} \Rightarrow \Delta A B C i s \text{ equilateral.}$

$\therefore a = b = c = 4.$