A transmitting antenna is kept on the surface of the earth. The...

The formula to calculate the range of the antenna is given by

$\gamma = \sqrt{2Rh} . . . \left(1\right)$

Substitute the values of the known parameters into equation (1) and solve to obtain the required height of the antenna.

$\begin{cases}4 \times {10}^{3} & = & \sqrt{2 \times 6400000 \times h} \\ ⇒ & 16 \times {10}^{6} = 2 \times 64 \times {10}^{5} \times h \\ ⇒ & h = \left(\dfrac{160}{2 \times 64}\right)m = \left(\dfrac{10}{8}\right)m \\ = & \dfrac{1000}{8} \times {10}^{- 2}m \\ = & 125 \times {10}^{- 2}m\end{cases}$