Question

Two poles of height 18 metres and 7 metres are erected on the ground.A wire of length 22 metres tied to the top of poles.
Find the angle made by wire with the horizontal.

Answer 1

$$\begin{gathered} \mathrm{Let}\mathrm{the}\mathrm{angle}\mathrm{of}\mathrm{elevation}\mathrm{from}\mathrm{the}\mathrm{top}\mathrm{of}\mathrm{the}\mathrm{first}\mathrm{pole}\mathrm{to}\mathrm{the}\mathrm{top}\mathrm{of}\mathrm{second}\mathrm{pole}\mathrm{be}\theta . \\ \mathrm{Given}:\mathrm{Height}\mathrm{of}\mathrm{the}\mathrm{first}\mathrm{pole},PQ=7\mathrm{m}\mathrm{and}\mathrm{height}\mathrm{of}\mathrm{the}\mathrm{second}\mathrm{pole},TR=18\mathrm{m} \\ \mathrm{Distance}\mathrm{between}\mathrm{the}\mathrm{top}\mathrm{of}\mathrm{the}\mathrm{first}\mathrm{pole}\mathrm{and}\mathrm{second}\mathrm{pole},PT=22\mathrm{m} \\ \mathrm{From}\mathrm{the}\mathrm{figure},PQ=SR=7\mathrm{m} \\ \therefore TS=TR-SR=(18-7)\mathrm{m}=11\mathrm{m} \\ \mathrm{Now},in△TSP,\mathrm{we}\mathrm{have}: \\ \sin \theta =\frac{\mathrm{perpendicular}}{\mathrm{hypotenuse}}=\frac{TS}{PT} \\ \Rightarrow \sin \theta =\frac{11}{22}=\frac{1}{2} \\ \Rightarrow \sin \theta =\sin 30° \\ \Rightarrow \theta =30° \\ \therefore \mathrm{The}\mathrm{angle}\mathrm{made}\mathrm{by}\mathrm{the}\mathrm{wire}\mathrm{with}\mathrm{the}\mathrm{horizontal}\mathrm{is}30°. \end{gathered}$$