Question

In ∆ABC, ∠B = 90°, ∠A = 30° and AB = 9 cm.
Then, BC = ?
(a) 3 cm
(b) $2\sqrt{3}\mathrm{cm}$
(c) $3\sqrt{3}\mathrm{cm}$
(d) 6 cm
Figure

Answer 1

(c ) $3\sqrt{3}\mathrm{cm}$

In right-angled ∆ ABC, we have:
$$\begin{gathered} \frac{BC}{AB}=\tan {30}^{\mathrm{o}}=\frac{1}{\sqrt{3}} \\ \Rightarrow BC=\frac{AB}{\sqrt{3}}=\frac{9}{\sqrt{3}}=3\sqrt{3}\mathrm{cm} \\ \therefore BC=3\sqrt{3}\mathrm{cm} \end{gathered}$$