**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.