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

Answer: Option A

Let AB and CD be two poles
AB = 20 m, CD = 14 m
A and C are joined by a wire
CE || DB and angle of elevation of A is 30°
Let CE = DB = x and AC = L

Now AE = AB - EB = AB - CD = 20 - 14 = 6 m
$$\begin{array}{rl}& \text{Now in right }\Delta ACE,\\ & \sin \theta =\frac{\text{Perpendicular}}{\text{Hypotenuse}}=\frac{AE}{AC}\\ & \Rightarrow \sin 30^{\circ }=\frac{6}{AC}\\ & \Rightarrow \frac{1}{2}=\frac{6}{AC}\\ & \Rightarrow AC=2\times 6=12\\ & \therefore \text{Length of AC}=12m\end{array}$$