A ladder is placed against a wall such that it just reaches the top of the wall. The foot of the ladder is 1.5 metres away from the wall and the ladder is inclined at an angle of 60° with the ground. Find the height of the wall.

Let MP be the wall of height h metres and O be the point on the ground 1.5 m away from the foot of the wall.

Then, the angle of elevation = ∠MOP = ∠60° (given).

In △OMP, ∠OMP = 90°.

From △OMP, we get

$\Rightarrow \text{tan 60°} = \dfrac{MP}{OM} \\[1em] \Rightarrow \sqrt{3} = \dfrac{h}{1.5} \\[1em] \Rightarrow h = 1.5 \times \sqrt{3} \\[1em] \Rightarrow h = 2.598 \approx 2.6$

Hence, the height of the tower = 2.6 m.