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,

$$\begin{gathered} \sin \theta =\frac{\mathrm{AE}}{\mathrm{AC}} \\ \Rightarrow \sin \theta =\frac{11}{22}=\frac{1}{2} \\ \Rightarrow \sin \theta =\frac{1}{2}=\sin 30° \\ \Rightarrow \theta =30° \end{gathered}$$
Thus, the angle made by the wire with the horizontal is 30º.