# The tops of two poles of height 20 m and 14 m are connected by a wire. If the wire makes an angle of 30° with horizontal, then the length of the wire is

A. 12 m B. 10 m C. 8 m D. 6 m Answer: Option A
Let PQ and RS be two poles PQ = 20 m, RS = 14 m S and P are joined by a wire ST || RQ and angle of elevation of P is 30° Let ST = RQ = x and SP = L $\begin{array}{l}\text{Now PT}=\text{PQ}-\text{QT}\\ \Rightarrow\text{PQ}-\text{RS}\\ =20-14=6\ \text{m}\\ \text{Now in right}\ \triangle\ \text{PST,}\\ \sin\theta=\frac{\text{ Perpendicular }}{\text{ Hypotenuse }}=\frac{\text{PT}}{\text{SP}}\\ \Rightarrow\sin30^{\circ}=\frac{6}{\text{SP}}\\ \Rightarrow\frac{1}{2}=\frac{6}{\text{SP}}\\ \Rightarrow\text{SP}=2\times6=12\\ \therefore\text{ Length of }\mathrm{AC}=12\mathrm{~m}\end{array}$