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 =

A. 26

B. 16

C. 12

D. 10

Answer: Option C

Solution(By Examveda Team)

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
$$\eqalign{ & {\text{Now}}\,{\text{in}}\,\Delta ACE \cr & \sin {30^ \circ } = \frac{{CE}}{{AC}} = \frac{6}{l} \cr & \Rightarrow \frac{1}{2} = \frac{6}{l} \cr & \Rightarrow l = 2 \times 6 = 12\,m \cr} $$