# 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

A. $15 \sqrt{3} m$ B. $\frac{15 \sqrt{3}}{2} m$ C. $\frac{15}{2} m$ D. $15 m$ Answer: Option B
Let AB is a wall and AC is the ladder 15 m long which makes an angle of 60° with the ground $\begin{array}{l}\therefore\text{In }\triangle\text{ABC,}\ \angle\text{B}=90^{\circ}\\ \text{Let height of wall AB}=\text{h}\\ \text{Then,}\\ \sin\theta=\frac{\text{AB}}{\text{AC}}\Rightarrow\sin60^{\circ}=\frac{\text{h}}{15}\\ \Rightarrow\frac{\sqrt{3}}{2}=\frac{\text{h}}{15}\\ \Rightarrow\text{h}=\frac{15\sqrt{3}}{2}\text{m}\\ \therefore\text{Height of the wall}\\ \frac{=15\sqrt{3}}{2}\text{m}\end{array}\begin{array}{l}\\ \end{array}$