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

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

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

$AB=6\sqrt{3}cm$

$sinA=sin{30}^{\circ }=\frac{BC}{AC}=\frac{6}{AC}$,

$\frac{1}{2}=\frac{6}{AC}$ $\because \sin 30°=\frac{1}{2}$

$AC=12cm$