Question

Find the unknown elements of $△ABC$ in which $a=\sqrt{3+1}$ ,$b=\sqrt{3-1}$, $c={60}^{\circ }$.

Answer 1

Given $a=2,b=\sqrt{2},c={60}^{\circ }$

$cosc=\frac{a^2+b^2+c^2}{2ab}$

$\Rightarrow cos{60}^{\circ }=\frac{4+2-c^2}{2\times 2\times \sqrt{2}}$

$\Rightarrow \frac{1}{2}=\frac{6-c^2}{2\times 2\times \sqrt{2}}$

$\Rightarrow 6-c^2=2\sqrt{2}$

$\Rightarrow c=\sqrt{6-2\sqrt{2}}$