At a particular station, the TV transmission tower has a height of 100 m . To triple its coverage range, height of the tower should be increased to

Step-by-step solution

Let d be range of TV transmission. From above figure, d 2 = h + R 2 - R 2 ⇒ d 2 = h 2 + R 2 + 2 R H - R 2 ⇒ d 2 = h 2 + 2 R h As R ≫ ≫ h then, d ≈ 2 R h           . . . 1 Now, if coverage is to be increased 3 times 3 d = 2 R h '         . . . 2 Dividing equation 2 by 1 , we have 3 d   d = 2 R h ' 2 R h ⇒ 9 = h ' h 9 h = h ' If h = 100   m , then tower of height 900   m is required.