The height of a transmitting antenna is $h_T=80\text{ m}$ and the receiving antenna is $h_R=45\text{ m}$. The maximum line-of-sight distance between them is (take radius of Earth as $R=6400\text{ km}$):

Solution

1. The formula for line-of-sight distance is $d=\sqrt{2R{h}_T}+\sqrt{2R{h}_R}$.
2. Given $R=6.4\times 10^6\text{ m}$, $h_T=80\text{ m}$, and $h_R=45\text{ m}$.
3. Calculating individual distances: $$\begin{array}{rl}{d}_T& =\sqrt{2\times 6.4\times 10^6\times 80}\\ & =32000\text{ m}\\ & =32\text{ km}\end{array}$$.
4. Calculating individual distances: $$\begin{array}{rl}{d}_R& =\sqrt{2\times 6.4\times 10^6\times 45}\\ & =24000\text{ m}\\ & =24\text{ km}\end{array}$$.
5. Total distance $$\begin{array}{rl}d& =32\text{ km}+24\text{ km}\\ & =56\text{ km}\end{array}$$.
6. Hence the answer is (C).