# 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

A. 12 m

B. 10 m

C. 8 m

D. 6 m

**Answer: Option A **

__Solution(By Examveda Team)__

Let AB and CD be two polesAB = 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

$$\eqalign{ & {\text{Now in right }}\Delta ACE, \cr & \sin \theta = \frac{{{\text{Perpendicular}}}}{{{\text{Hypotenuse}}}} = \frac{{AE}}{{AC}} \cr & \Rightarrow \sin {30^ \circ } = \frac{6}{{AC}} \cr & \Rightarrow \frac{1}{2} = \frac{6}{{AC}} \cr & \Rightarrow AC = 2 \times 6 = 12 \cr & \therefore {\text{Length of AC}} = 12\,m \cr} $$

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it was helpfull for my 10 exam tq so much