Question

In a $\Delta$ABC, $2\sin A+\sqrt{3}\sin B=\frac{5}{2}$ and $\sqrt{3}\sin A+2\sin B=\frac{3\sqrt{3}}{2}$ then C$=$?

• A. ${15}^o$
• B. ${45}^o$
• C. ${60}^o$
• D. ${90}^o$

Answer 1

The correct option is D ${90}^o$

$2\sin A+\sqrt{3}\sin B=\frac{5}{2}$

$\sqrt{3}\sin A+2\sin B=\frac{3\sqrt{3}}{2}$

Solving above two equations we get,

$\sin A=5-\frac{9}{2}=\frac{1}{2}⟹A={30}^{\circ }$

$\sin B=\frac{1}{\sqrt{3}}(-1+\frac{5}{2})=\frac{\sqrt{3}}{2}⟹B={60}^{\circ }$

$⟹C={180}^{\circ }-{90}^{\circ }={90}^{\circ }$