The tops of two poles of heights $\displaystyle 20$ m and $\displaystyle 28$ m are connected with a wire. The wire is inclined to the horizontal at an angle of $\displaystyle 30$°. Find the length of the wire and the distance between the two poles.

\[\begin{array}{r} A E=8 \mathrm{~m} \\ \sin 30^{\circ}=\frac{1}{2}=\frac{A E}{A C} \\ \Rightarrow A C=16 \mathrm{~m} \text { (length of wire) } \\ \cos 30^{\circ}=\frac{\sqrt{3}}{2}=\frac{x}{16} \\ \Rightarrow x=8 \sqrt{3} \mathrm{~m} \end{array} \] ∴ The distance between two poles $\displaystyle =8 \sqrt{ } 3 \mathrm{~m}$