\(d ^{2}=( h + R )^{2}- R ^{2}\)

\(= h ^{2}+ R ^{2}+2 RH - R ^{2}\)

\(d ^{2}= h ^{2}+2 Rh\)

\(\text { as } R \gg \gg \text { h then }\)

\(d \approx \sqrt{2 Rh } . \ldots . \text { (1) }\)

Now, if coverage is to be increased \(3\) times

\(3 d =\sqrt{2 Rh ^{\prime}} \ldots \text {. (2) }\)

Divide \(2\) and \(1 \frac{3 d }{ d }=\sqrt{\frac{2 R h^{\prime}}{2 R h}}\)

\(9=\frac{ h ^{\prime}}{ h }\)

\(9\,h = h \text { ' }\)

\(\text { If } h =100 m \text { then tower of height } 900 m \text { is } \text { required }\)