Question

A ladder 15 m long just reaches the top of a vertical wall. If the ladder makes an angle of ${60}^{\circ }$ with the wall, then find the height of the wall.

Answer 1

Given that, the height of the ladder = 15 m

Let the height of the vertical wall = h

And the ladder makes an angle of elevation ${60}^{\circ }$ with the wall i.e., $\theta ={60}^{\circ }$

In $\Delta QRP,\cos {60}^{\circ }=\frac{PR}{PQ}=\frac{h}{15}$

$\Rightarrow \frac{1}{2}=\frac{h}{15}$ [$\because \cos {60}^{\circ }=\frac{1}{2}$]

$\Rightarrow h=\frac{15}{2}=7.5m$

Hence, the required height of the wall is $\frac{15}{2}=7.5m$.