Question

The maximum distance between the transmitting and receiving TV towers is $72km$. If the ratio of the heights of the TV transmitting tower to receiving tower is $16:25$, the heights of the transmitting and receiving towers are

• A. $50cm;80m$
• B. $40cm;80m$
• C. $80cm;125m$
• D. $25cm;75m$

Answer 1

The correct option is A $50cm;80m$

As we know

$d_{max}=\sqrt{2R{H}_T}+\sqrt{2R{H}_R}=72km$

$\frac{H_T}{H_R}=\frac{16}{25}$

$⟹\sqrt{\frac{2R{H}_R\times 16}{25}}+\sqrt{2R{H}_R}=72$

$⟹\sqrt{2R{H}_R}(\frac{4}{5}+1)=72\times {10}^{3}m$

$⟹\sqrt{2\times 6400\times {10}^3{H}_R}=72\left(\frac{5}{9}\right)\times {10}^3$

$⟹H_R=125m$ and $H_T=80m$