Question

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

Answer 1

Let AB and CD represent the heights of the wire .

Draw seg AM ⊥ seg CD. 

Angle of elevation = ∠CAM = θ 

AB = 7 m 

CD = 18 m 

AC = 22 m 

In □ABDM, 

∠B = ∠D = 90° 

∠M = 90° …[seg AM ⊥ seg CD] 

∴ ∠A = 90° … [Remaining angle of □ABDM]

∴ □ABDM is a rectangle. … [Each angle is 90°] 

∴ DM = AB = 7 m … [Opposite sides of a rectangle] 

Now, CD = CM + DM … [C – M – D] 

∴ 18 = CM + 7 

∴ CM = 18 – 7 = 11 m 

In right angled ∆AMC, 

sin θ = CM/AC  …..[By definition] 

∴ sin θ = 11/22 = 1/2  

But, sin 30° = 1/2 

∴ θ = 30° 

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