Question

In a triangle ABC , if $a=2,B={60}^{o}andC={75}^o$, then $b=$

Answer 1

In triangle ABC,

$a=2$

$B={60}^{\circ }$

$C={75}^{\circ }$

$b=?$

Angle $A={180}^{\circ }-B-C$$={45}^{\circ }$

Now in a triangle,

$\frac{\sin A}{a}=\frac{\sin B}{b}=\frac{\sin C}{c}$

So,

$\frac{\sin {45}^{\circ }}{2}=\frac{\sin {60}^{\circ }}{b}$

$\frac{1}{2\sqrt{2}}=\frac{\sqrt{3}}{2b}$

$b=\sqrt{3}\times \sqrt{2}=\sqrt{6}$