Two antennas A and B have maximum line of sight range $R_{AB}=45.5 km$. If the height of antenna A is 32 m then the height of antenna B is: (Given radius of earth is = 6400 km)

50 m

The correct answer is Option (3) → 50 m

Given,

$R_{AB}$, total line of sight distance = 45.5 km

R, Radius of earth = $6.4×10^6m$

$h_A$, height of Antenna A = 32 m

$h_B$, height of Antenna B

$R_{AB}=\sqrt{2RH_A}+\sqrt{2RH_B}$ [formula]

$45.5×10^3=\sqrt{2×6.4×10^6×32}+\sqrt{2×6.4×10^6×h_B}$

$45500=20238.22+\sqrt{2×6.4×10^6×h_B}$

$\sqrt{2×6.4×10^6×h_B}=45500-20238.22$

$2×6.4×10^6×h_B=637194351.4$

$h_B=\frac{637194351.4}{2×6.4×10^6}=49.78m$