Two poles of heights 18 metre and 7 metre are erected on a ground. The

1.	Two poles of heights 18 metre and 7 metre are erected on a ground. The length of thewire fastened at their tops in 22 metre. Find the angle made by the wire with thehorizontal.
Answer» seg AB and CD represents two poles. AB = 18 m, CD = 7 m seg AC represent the length of the wire. AC = 22 m □EBDC is a rectangle ∴ EB = CD = 7 m [Opposite sides of rectangle] AB = AE + EB [∵ A - E - B] ∴ 18 = AE + 7 ∴ 18 – 7 = AE ∴ AE = 11 m In right angled ∆ AEC, sin C = opposite side of ∠C/Hypotenuse ∴ sin C = AE/AC ∴ sin C = 11/22 ∴ sin C = ½ .........(i) But, sin 30º = ½ ......(ii) From equation (i) and (ii), we can conclude that sin C = sin 30º ∴ ∠C = 30º ∴The angle made by the wire with horizontal is 30º.

Two poles of heights 18 metre and 7 metre are erected on a ground. The length of thewire fastened at their tops in 22 metre. Find the angle made by the wire with thehorizontal.

Answer»

seg AB and CD represents two poles. AB = 18 m, CD = 7 m

seg AC represent the length of the wire. AC = 22 m

□EBDC is a rectangle

∴ EB = CD = 7 m [Opposite sides of rectangle]

AB = AE + EB [∵ A - E - B]

∴ 18 = AE + 7

∴ 18 – 7 = AE

∴ AE = 11 m

In right angled ∆ AEC,

sin C = opposite side of ∠C/Hypotenuse

∴ sin C = AE/AC

∴ sin C = 11/22

∴ sin C = ½ .........(i)

But,

sin 30º = ½ ......(ii)

From equation (i) and (ii), we can conclude that

sin C = sin 30º

∴ ∠C = 30º

∴The angle made by the wire with horizontal is 30º.