Question

The ladder resting against a vertical wall is inclined at an angle of 30${}^{\circ }$ to the ground. The foot of the ladder is 9 m away from the wall. Find the length of the ladder.

Answer 1

The situation is represented by the figure below

Here, $cos\left(\angle ACB\right)=\frac{BC}{AC}\Rightarrow AC=\frac{BC}{cos\left(\angle ACB\right)}=\frac{9}{cos{30}^{\circ }}=\frac{9}{\frac{\sqrt{3}}{2}}=\frac{18}{\sqrt{3}}=6\sqrt{3}\therefore lengthofladder=6\sqrt{3}m$