Find the area

Explanation

Television signal waves have the frequency range 80 MHZ these waves neither follow the curvature of the earth nor get reflected by ionosphere. The propagation of such wave is possible only via satellite or by using all receiver antenna which may direct intercept the transmitted signals coming from the transmitter antenna In order to find the height of a transmitter for a greater coverage let us consider a TV transmitting antenna of high h located at A on the surface of the earth. The transmitted signal can be received within a circle of radius PB (or PC) on the surface of the earth as shown in the figure.Let R be the radius of the earth, then from the geometry of the fig. we have PB=PC=d, AP=h, `therefore` OP=OA+AP=R+h, and in right angle triangle POB, `OP^(2)=PB^(2)+BO^(2) or ` (R+h)^(2)=d^(2)+R^(2)` or `d^(2)=h^(2)+2Rh,If R, then neglecting `h square H^(2)`, we have `d^(2)=2Rh`.Thus a T.V signal will cover the area=`pi d^(2)=2pi Rh`