Question

A ladder 15 m long just reaches the top of a vertical wall. If the ladder makes an angle of 60° with the wall, then the height of the wall is

(a) $15\sqrt{3}\mathrm{m}$ (b) $\frac{15\sqrt{3}}{2}\mathrm{m}$ (c) $\frac{15}{2}$ m (d) 15 m [CBSE 2013]

Answer 1

Suppose AB is the wall and AC is the ladder.

It is given that, AC = 15 m and $\angle$CAB = 60°.

In right ∆ABC,

$$\begin{gathered} \cos 60°=\frac{\mathrm{AB}}{\mathrm{AC}} \\ \Rightarrow \frac{1}{2}=\frac{\mathrm{AB}}{15} \\ \Rightarrow \mathrm{AB}=\frac{15}{2}\mathrm{m} \end{gathered}$$

Thus, the height of the wall is $\frac{15}{2}$ m.

Hence, the correct answer is option C.