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. $51.2m$, $80m$
• B. $40m$, $80m$
• C. $80m$, $125m$
• D. $25m$, $75m$

Answer 1

The correct option is C $80m$, $125m$

$d_{max}=\sqrt{2R{H}_T}+\sqrt{2R{H}_R}=72km\frac{H_T}{H_R}=\frac{16}{25}\Rightarrow \sqrt{\frac{2R{H}_R\times 16}{25}}+\sqrt{2R{H}_R}=72\Rightarrow \frac{4\sqrt{2R{H}_R}}{5}+\sqrt{2R{H}_R}=72\Rightarrow (1+\frac{4}{5})\sqrt{2R{H}_R}=72\Rightarrow \sqrt{2R{H}_R}=72\left(\frac{5}{9}\right)=40\Rightarrow H_R=125mand{H}_T=80m$