4. 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 the poles. Find the angle made by the wire with the horizontal.
Sol. 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.