Question

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

In a ∆ABC, if b = $\sqrt{3}$, c = 1 and $\angle A=30°$, find a.

Answer 1

In ∆ABC, b = $\sqrt{3}$, c = 1 and $\angle A=30°$.

Using cosine formula, we have

$$\begin{gathered} \cos A=\frac{b^2+c^2-a^2}{2bc} \\ \Rightarrow \cos 30°=\frac{{\left(\sqrt{3}\right)}^2+{\left(1\right)}^2-a^2}{2\times \sqrt{3}\times 1} \\ \Rightarrow \frac{\sqrt{3}}{2}=\frac{4-a^2}{2\sqrt{3}} \\ \Rightarrow 3=4-a^2 \\ \Rightarrow a^2=4-3=1 \\ \Rightarrow a=1 \end{gathered}$$