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# A transmission tower at a particular place has a height of 135m. (A) What is its coverage range? (B) By how much should the height be increased to 2 times its coverage range? Given that radius of earth = 6400 km.

Let $h$ be height of tower, $d$ be radius of coverage, and $R$ the radius of earth $\rightarrow$ $d=\sqrt{2Rh}$
Given $R = 6400 \;km$, and $h = 135\;m$, $d = \sqrt {2 \times 6400 \times 10^3 \times 135} = 41.57\;km$
To calculate the new height to increase the coverage, $\rightarrow \large\frac{d_1}{d_2}$$= \sqrt {\large\frac{h_1}{h2}} Given d_2 = 2\times d_1 and h_1 = 135\;m, we can calculate h_2 = 135\times \large\frac{2^2}{1^1}$$ = 540\;m$

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