Answer each of the following questions in one word or one sentence or as per exact requirement of the question.
Question:
Answer each of the following questions in one word or one sentence or as per exact requirement of the question.
In a $\triangle \mathrm{ABC}$, if $b=\sqrt{3}, c=1$ and $\angle A=30^{\circ}$, find $a$.
Solution:
In $\triangle \mathrm{ABC}, b=\sqrt{3}, c=1$ and $\angle A=30^{\circ}$.
Using cosine formula, we have
$\cos A=\frac{b^{2}+c^{2}-a^{2}}{2 b c}$
$\Rightarrow \cos 30^{\circ}=\frac{(\sqrt{3})^{2}+(1)^{2}-a^{2}}{2 \times \sqrt{3} \times 1}$
$\Rightarrow \frac{\sqrt{3}}{2}=\frac{4-a^{2}}{2 \sqrt{3}}$
$\Rightarrow 3=4-a^{2}$
$\Rightarrow a^{2}=4-3=1$
$\Rightarrow a=1$