Question

In right-angled traingle ABC, ∠B=90∘. Then the magnitude of angle A, if AB is √3 times of BC is

• A. ${30}^{\circ }$
• B. ${60}^{\circ }$
• C. ${45}^{\circ }$
• D. ${75}^{\circ }$

Answer 1

The correct option is A ${30}^{\circ }$


It is given that AB = $\sqrt{3}$ times BC

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

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

But $\frac{BC}{AB}$ = tan A

$\therefore$ tan A = $\frac{1}{\sqrt{3}}$

Hence, $\angle A$ = ${30}^{\circ }$