Question

Answer each of the following questions in one word or one sentence or as per exact requirement of for question:

$Ina\Delta ABC,ifb=\sqrt{3},c=1and\angle A={30}^{\circ },finda$

Answer 1

$\text{We know,}cosA=\frac{b^2+c^2-a^2}{2bc}\Rightarrow cos30=\frac{{\sqrt{3}}^2+1^2-a^2}{2\times \sqrt{3}\times 1}\Rightarrow \frac{\sqrt{3}}{2}=\frac{3+1-a^2}{2\sqrt{3}}\Rightarrow 2\sqrt{3}\times \sqrt{3}=2(4-a^2)\Rightarrow 3=4-a^2\Rightarrow a^2=1\Rightarrow a=1$