A ladder 15 m long just reaches the top of a vertical wall.
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) $\frac{15}{2} \mathrm{~m}$

(d) $15 \mathrm{~m}$

Solution:

Suppose AB is the wall and AC is the ladder.

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

In right ∆ABC,

$\cos 60^{\circ}=\frac{\mathrm{AB}}{\mathrm{AC}}$

$\Rightarrow \frac{1}{2}=\frac{\mathrm{AB}}{15}$

$\Rightarrow \mathrm{AB}=\frac{15}{2} \mathrm{~m}$

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

Hence, the correct answer is option C.