The tops of two poles of height 16 m and 10 m are connected by a wire of length l metres. If the wire makes an angle of 30° with the horizontal, then l =

Answer: Option C

Let AB and CD are two poles AB = 10 m and CD = 16 m

AC is wire which makes an angle of 30° with the horizontal
Let BD = x, then AE = x
CE = CD - ED = CD - AB = 16 - 10 = 6m
$$\begin{array}{rl}& \text{Now}\text{in}\Delta ACE\\ & \sin 30^{\circ }=\frac{CE}{AC}=\frac{6}{l}\\ & \Rightarrow \frac{1}{2}=\frac{6}{l}\\ & \Rightarrow l=2\times 6=12m\end{array}$$