Question

In $△$ABC, right angled at B, BC = 5 cm, $\angle$ BAC = ${30}^{\circ }$ , find the length of the sides AB and AC.

Answer 1

We are gven

∠ BAC = ${30}^{\circ }$ , i.e , ∠A = ${30}^{\circ }$

and BC = 5cm

Now sinA = $\frac{BC}{AC}$ or sin ${30}^{\circ }$ = $\frac{5}{AC}$

or $\frac{5}{AC}$ = $\frac{1}{2}$ ........ [ ∵ sin ${30}^{\circ }$ = $\frac{1}{2}$ ]\

or AC = 2 × 5 or 10 cm

To find AB , we have

$\frac{AB}{AC}$ = cos A

or $\frac{AB}{10}$ = cos ${30}^{\circ }$

or $\frac{AB}{10}$ = $\frac{\sqrt{3}}{2}$

∴ AB = $\frac{\sqrt{3}}{2}$ × 10 or 5 $\sqrt{3}$ cm

Hence, AB = 5 $\sqrt{3}$ cm and AC = 10 cm