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

Answer: Option B

Let AB is a wall and AC is the ladder 15 m long which makes an angle of 60° with the ground

∴ In ∆ABC, ∠B = 90°
Let height of wall AB = h
Then
$$\sin \theta =\frac{AB}{AC}\Rightarrow \sin 60^{\circ }=\frac{h}{15}$$
$$\begin{array}{rl}& \Rightarrow \frac{\sqrt{3}}{2}=\frac{h}{15}\\ & \Rightarrow h=\frac{15\sqrt{3}}{2}m\end{array}$$
∴ Height of the wall $$=\frac{15\sqrt{3}}{2}m$$