Question

In the adjoining figure, $ABC$ is a right triangle right angled at $B$. If $AB=10cm$ and $\angle C={30}^{\circ }$, then the length of the side $BC$ is

• A. $\frac{10}{\sqrt{3}}cm$
• B. $10\sqrt{3}cm$
• C. $20cm$
• D. $5cm$

Answer 1

The correct option is B $10\sqrt{3}cm$

In the given $△ABC\angle C={30}^{\circ }and\angle B={90}^{\circ }$

Sum of all angles is ${180}^{\circ }$

$\therefore \angle A={180}^{\circ }-({30}^{\circ }+{90}^{\circ })$

$\therefore \angle A={180}^{\circ }-{120}^{\circ }$

$\therefore \angle A={60}^{\circ }$

$tan{60}^{\circ }=\frac{BC}{AB}$

$\sqrt{3}=\frac{BC}{10}$

$BC=10\times \sqrt{3}$

$\therefore BC=10\sqrt{3}$