Coherent and Incoherent Addition of Waves

A transmitting antenna at the top of a tower has a height $32 \mathrm{m}$ and the height of the receiving antenna is $50 \mathrm{m}$. What is the maximum distance between two such antenna for satisfactory communication in line-of-sight (LOS) mode? Given the radius of earth is $6.4\times {10}^6\mathrm{m}$.

Prove that the superposition of two waves from two coherent sources having displacements ${\mathrm{y}}_1=\mathrm{a} \mathrm{sin\omega t}$ and ${\mathrm{y}}_2=\mathrm{a} \sin \left(\mathrm{\omega t}+\mathrm{\varphi }\right)$ at a point produce the resultant intensity $\mathrm{I}=4{\mathrm{a}}^2{\cos }^2\frac{\mathrm{\varphi }}{2}$.