Question

Mark the correct alternative in each of the following :

$Ina\Delta ABC,ifa=2,\angle B={60}^{\circ }and\angle C={75}^{\circ },thenb=$

• A. $\sqrt{3}$
• B. $\sqrt{6}$
• C. $\sqrt{9}$
• D. $\sqrt{2}$

Answer 1

The correct option is B

$\sqrt{6}$

$\text{We know,}A+B+C=\pi \therefore A=\pi -(B+C)\Rightarrow A={180}^{\circ }-({60}^{\circ }+{75}^{\circ })={45}^{\circ }\text{Now},\text{according to sine rule},\frac{a}{sinA}=\frac{b}{sinB}\Rightarrow \frac{2}{sin{45}^{\circ }}=\frac{b}{sin{60}^{\circ }}[\because a=2,\angle B={45}^{\circ }]\Rightarrow \frac{2}{\frac{\sqrt{2}}{2}}=\frac{b}{\frac{\sqrt{3}}{2}}=\frac{4}{\sqrt{2}}\times \frac{\sqrt{3}}{2}=b\text{Hnece,}b=\sqrt{6}$