Question

In a $\Delta ABC,\frac{a}{b}=2+\sqrt{3}$ and $\left(\angle A,\angle B\right)$ is equal to:

• A. $\left({105}^0,{15}^0\right)$
• B. $\left({45}^0,{75}^0\right)$
• C. $\left({15}^0,{105}^0\right)$
• D. $\left({75}^0,{45}^0\right)$

Answer 1

The correct option is A $\left({105}^0,{15}^0\right)$

Given,

$\frac{a}{b}=2+\sqrt{3}$

Using sine rule,

$\frac{a}{sinA}=\frac{b}{sinB}⟹\frac{a}{b}=\frac{SinA}{SinB}$

$⟹\frac{SinA}{SinB}=2+\sqrt{3}$

$⟹\frac{SinA}{SinB}=tan75$

$⟹tan75=\frac{sin75}{cos75}=\frac{sin(90+15)}{sin(90-15}=\frac{sin105}{sin15}$

As $\angle C=60$

$\therefore \angle A+\angle B=120$

so $\angle A={105}^{\circ },B={15}^{\circ }$