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

Let d be range

$\begin{array}{l}{\mathrm{d}}^2=(\mathrm{h}+\mathrm{R}{)}^2-{\mathrm{R}}^2\\ ={\mathrm{h}}^2+{\mathrm{R}}^2+2\mathrm{RH}-{\mathrm{R}}^2\\ {\mathrm{d}}^2={\mathrm{h}}^2+2\mathrm{Rh}\\ \text{ as }\mathrm{R}\gg \gg \text{ h then }\\ \mathrm{d}\approx \sqrt{2\mathrm{Rh}} \dots .\left(1\right)\end{array}$

Now, if coverage is to be increased 3 times

$3\mathrm{d}=\sqrt{2{\mathrm{Rh}}^{\mathrm{\prime }}} ....\left(2\right)$

Divide 2 and 1 

$\frac{3\mathrm{d}}{\mathrm{d}}=\sqrt{\frac{2{\mathrm{Rh}}^{\mathrm{\prime }}}{2\mathrm{Rh}}}$

$\begin{array}{l}9=\frac{{\mathrm{h}}^{\mathrm{\prime }}}{\mathrm{h}}\\ 9\mathrm{h}={\mathrm{h}}^{\mathrm{\prime }}\end{array}$

If h = 100 m then tower of height 900 m is required