Deduce an expression for the distance upto which the TV signal can be directly received from a TV tower of height h.

LetT.V. signal be transmitted from an antenna of height . here R =radius of earth, OS = OT=OP, PQ=h,OQ=OP+PQ=R+h

In right angle triangle QPS, $S{Q}^2=S{P}^2+P{Q}^2=d^2+h^2$
In right angle triangle OSQ= $$\begin{gathered} o{Q}^2=o{s}^2+S{Q}^2 \\ (R+h{)}^2=R^2+d^2+h^2 \end{gathered}$$

$$\begin{gathered} d^2=2hR \\ d=\sqrt{2hR} \end{gathered}$$