Question

A ladder rests against a wall so that its top touches the roof of the house. If the ladder makes an angle of ${60}^{\circ }$ with the horizontal and height of the house be $6\sqrt{3}\text{m}$, then the length of the ladder is:

• A. $12\sqrt{3}\text{m}$
• B. $12\text{m}$
• C. $\frac{12}{\sqrt{3}}\text{m}$
• D. None of these

Answer 1

The correct option is B $12\text{m}$

From the question, we can say
$\sin {60}^o=\frac{BC}{AC}$

Length of ladder, $AC=\frac{6\sqrt{3}}{\sin {60}^{\circ }}=\frac{6\sqrt{3}}{\frac{\sqrt{3}}{2}}=12\text{m}$