What should be the height of a transmitting antenna for a TV telecast to cover a radius of 128 km? 

Dear Student ,
Here in this case let us take that ,range = d= 128 km, height = h and radius of earth = r = 6400 km .
$$\begin{gathered} Now ,d=\sqrt{2hR} \\ \Rightarrow h=\frac{d^2}{2R}=\frac{128\times 128}{2\times 6400} \\ \Rightarrow h=1.28 km \end{gathered}$$
Regards