Question

In a triangle abc if angle a is 60° and



b.c = (√3 + 1) : 2

Answer 1

$(\sqrt{3} + 1)x \: + 2x + 60 = 180$
$\sqrt{3} x + 1x + 2x = 120 \\ \sqrt{3} x \: + 3x = 120 \\ \sqrt{3}x(1 + \sqrt{3} ) = 120 \\ \sqrt{3} x = \frac{120}{1 + \sqrt{3} } \\ x = \frac{40 \sqrt{3} \times \sqrt{3} }{1 + \sqrt{3} ( \sqrt{3}) } \\ x = \frac{40 \sqrt{3} }{ \sqrt{3} + 1} \times \frac{ \sqrt{3} - 1}{ \sqrt{3} - 1} \\ x = \frac{40(3 - \sqrt{3}) }{3 - 1 } \\ x = 20(3 - \sqrt{3} )$
this is how its done