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
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.