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

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
$$\sin \theta = \frac{{AB}}{{AC}} \Rightarrow \sin {60^ \circ } = \frac{h}{{15}}$$
$$\eqalign{ & \Rightarrow \frac{{\sqrt 3 }}{2} = \frac{h}{{15}} \cr & \Rightarrow h = \frac{{15\sqrt 3 }}{2}\,m \cr} $$
∴ Height of the wall $$ = \frac{{15\sqrt 3 }}{2}\,m$$