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. Find the height of the wall.

Answer 1

Let the length of the ladder be $=15$m(hypotenuse)

The angle between the ladder and the wall $\angle BCA={60}^{\circ }$

Angle between ladder and the ground $\angle CAB={90}^{\circ }-{60}^{\circ }={30}^{\circ }$

Height of the wall $=BC$

$\sin {30}^{\circ }=\frac{BC}{15}$

$\Rightarrow \frac{1}{2}=\frac{BC}{15}$

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