Question

A ladder makes an angle of 60º with the ground when placed against a wall. If the foot of the ladder is 2 m away from the wall, then the length of the ladder (in metres) is

(a) $\frac{4}{\sqrt{3}}$ (b) $4\sqrt{3}$ (c) $2\sqrt{2}$ (d) $4$ [CBSE 2014]

Answer 1

Suppose AC is the ladder and BC is the distance of the foot of the ladder from the wall.

It is given that, BC = 2 m and $\angle$ACB = 60°.

In right ∆ABC,

$$\begin{gathered} \cos 60°=\frac{\mathrm{BC}}{\mathrm{AC}} \\ \Rightarrow \frac{1}{2}=\frac{2}{\mathrm{AC}} \\ \Rightarrow \mathrm{AC}=4\mathrm{m} \end{gathered}$$

Thus, the length of the ladder is 4 m.

Hence, the correct answer is option D.