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.

Answer 1

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.