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Question
Two poles of heights 18 metre and 7 metre are erected on a ground. The length of the wire fastened at their tops in 22 metre. Find the angle made by the wire with the horizontal.
Solution
Let AB and CD be the two poles standing on the ground.
Suppose the angle made by the wire with the horizontal be θ.
Here, AB = 18 m and CD = 7 m.
Length of the wire fastened at their tops = AC = 22 m
AE = AB − EB = 18 − 7 = 11 m (EB = CD)
In right ∆AEC,
\[\sin\theta = \frac{AE}{AC}\]
\[ \Rightarrow \sin\theta = \frac{11}{22} = \frac{1}{2}\]
\[ \Rightarrow \sin\theta = \frac{1}{2} = \sin30^\circ\]
\[ \Rightarrow \theta = 30^\circ\]
Thus, the angle made by the wire with the horizontal is 30º.
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