Question

If two sides and included angle of a triangle are $3+\sqrt{3},3-\sqrt{3}$ and ${60}^o$ respectively then find its third side.

Answer 1

$c^2=a^2+b^2-2ab\cos \theta$

$=(3-\sqrt{3}{)}^2+(3-\sqrt{3}{)}^2-2(9-3)\cos \theta 0^o$

$=9+9+3+3-2\times 6\times 2$

$=18+6-6=18$