Question

In a right angled $△ABD,\angle B={60}^o$ and $\angle A={30}^o$.

Then $\cos {30}^o$ is equal to:

• A. $\frac{\sqrt{3}}{2}$
• B. $\frac{1}{\sqrt{3}}$
• C. $\frac{2}{\sqrt{3}}$
• D. $\sqrt{3}$

Answer 1

The correct option is A $\frac{\sqrt{3}}{2}$

Consider an equilateral $△ABC$ with each side $=2a$.

So, each angle of $△ABC={60}^o$.

From $A$ draw $AD\perp BC$, so $BD=DC=a,\angle ADB={90}^o,\angle BAD={30}^o$.

From right angled $△ADB$, we have

$AD=\sqrt{{AB}^2-{BD}^2}=\sqrt{{\left(2a\right)}^2-a^2}=\sqrt{{4a}^2-a^2}=\sqrt{{3a}^2}=\sqrt{3}a$.

$\cos {30}^o=\frac{AD}{AB}=\frac{\sqrt{3}a}{2a}=\frac{\sqrt{3}}{2}$.

So, $\frac{\sqrt{3}}{2}$ is correct.