Question

$△$ ABC, right angled at B, BC = 6 cm and ∠ABC = ${30}^{\circ }$. Determine the length of the side AB and AC.

• A. 6$\sqrt{3}$ cm , 12cm
• B. 4$\sqrt{3}$ cm , 12cm
• C. 2$\sqrt{3}$ cm , 16cm
• D. $\sqrt{3}$ cm , 16cm

Answer 1

The correct option is A

6$\sqrt{3}$ cm , 12cm

We know, BC = 6cm

In $△$ ABC, tan A = tan ${30}^{\circ }$ = $\frac{BC}{AB}$ = $\frac{6}{AB}$

$\frac{1}{\sqrt{3}}$ = $\frac{6}{AB}$

AB = 6$\sqrt{3}$ cm

Sin A = Sin ${30}^{\circ }$ = $\frac{BC}{AC}$ = $\frac{6}{AC}$,

AC = 12cm