In the right-angled triangle ABC, ∠C = 90° and ∠B = 60°. If AC = 6 cm, find the lengths of the sides BC and AB.

From figure,

$\text{sin 60°} = \dfrac{\text{Perpendicular}}{\text{Hypotenuse}} \\[1em] \Rightarrow \dfrac{\sqrt{3}}{2} = \dfrac{AC}{AB} \\[1em] \Rightarrow \dfrac{\sqrt{3}}{2} = \dfrac{6}{AB} \\[1em] \Rightarrow AB = \dfrac{12}{\sqrt{3}} \\[1em] \Rightarrow AB = \dfrac{12}{\sqrt{3}} \times \dfrac{\sqrt{3}}{\sqrt{3}} \\[1em] \Rightarrow AB = \dfrac{12\sqrt{3}}{3} \\[1em] \Rightarrow AB = 4\sqrt{3} \text{ cm}. \\[1em] \text{tan 60°} = \dfrac{\text{Perpendicular}}{\text{Base}} \\[1em] \Rightarrow \sqrt{3} = \dfrac{AC}{BC} \\[1em] \Rightarrow \sqrt{3} = \dfrac{6}{BC} \\[1em] \Rightarrow BC = \dfrac{6}{\sqrt{3}} = 2\sqrt{3}.$

Hence, AB = $4\sqrt{3}$ cm and BC = $2\sqrt{3}$ cm.