Question

Choose the correct answer of the following 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) $15\sqrt{3}$ m (b) $\frac{15\sqrt{3}}{2}$m (c) $\frac{15}{2}$ m (d) 15 m [CBSE 2013]

Answer 1

Let AB be the wall and AC be the ladder.

We have,

$$\begin{gathered} \mathrm{AC}=15\mathrm{m}\mathrm{and}\angle \mathrm{BAC}=60° \\ \mathrm{In}∆\mathrm{ABC}, \\ \cos 60°=\frac{\mathrm{AB}}{\mathrm{AC}} \\ \Rightarrow \frac{1}{2}=\frac{\mathrm{AB}}{15} \\ \therefore \mathrm{AB}=\frac{15}{2}\mathrm{m} \end{gathered}$$

Hence, the correct answer is option (c).