Question

In the following figure $AB\perp BC$ and $\angle ACB={30}^{\circ }$, given $BC=\sqrt{300}m$. The length of $AB$ is

• A. $10m$
• B. $100m$
• C. $10\sqrt{3}m$
• D. $100\sqrt{3}m$

Answer 1

The correct option is A $10m$

Given that:

From the fig; $AB\perp BC,\angle ACB={30}^{\circ },BC=\sqrt{3}00m$

To find:

$AB=?$

Solution:

In $△ABC,$

$\tan \angle ACB=\frac{AB}{BC}$

or, $\tan {30}^{\circ }=\frac{AB}{BC}$

or, $AB=\tan {30}^{\circ }\times BC$

or, $AB=\frac{1}{\sqrt{3}}\times \sqrt{300}m$

or, $AB=\frac{1}{\sqrt{3}}\times 10\sqrt{3}m$

or, $AB=10m$

Therefore, A is the correct option.