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

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Let AB and CD be the poles such that AB = 16 m and CD = 10 m. The given information can be represented as Here, AC is the length of wire which is l. Also, AE = AB − BE = 16 m − 10 m = 6 m We have to find the length of wire l . So we use trigonometric ratios. In triangle ACE, sin C= (AE)/(EC) $\Rightarrow$ sin $30^\circ$=6/l $\Rightarrow$$\frac{1}{2}$=6/l $\Rightarrow$ l=12 [Solution diagram: 63584_solution_1.png]

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