A ladder is placed along a wall such that its upper end is resting against a vertical wall. The foot of the ladder is 2.4 m from the wall and the ladder is making an angle of 68° with the ground. Find the height, up to which the ladder reaches.

Let AC be the ladder and height of wall upto which ladder reaches be h meters.

∴ AB = h meters and BC = 2.4 meters.

Given,

Ladder is making an angle of 68° with the ground.

From figure,

In △ABC,

$\Rightarrow \text{tan θ} = \dfrac{\text{Perpendicular}}{\text{Base}} \\[1em] \Rightarrow \text{tan 68°} = \dfrac{AB}{BC} \\[1em] \Rightarrow 2.475 = \dfrac{h}{2.4} \\[1em] \Rightarrow h = 2.4 \times 2.475 \\[1em] \Rightarrow h = 5.94 \text{ m}.$

Hence, the ladder reaches upto a height of 5.94 m.