By what percentage will the transmission range of a TV tower be affected when the height of the tower is increased by 21%?

Given that the height of the tower is increased by 21%

$\Rightarrow \frac{{\mathrm{h}}^1-\mathrm{h}}{\mathrm{h}}=\frac{21}{100}\Rightarrow {\mathrm{h}}^1=\frac{121\mathrm{h}}{100}$

Let initial transmission range be d,

W.K.T,

$\mathrm{d}=\sqrt{2\times \mathrm{h}\times {\mathrm{r}}_{\mathrm{e}}}$

(r_e= radius of earth)

Let the new transmission range be d¹,

${\mathrm{d}}^1=\sqrt{2{\mathrm{h}}^1\times {\mathrm{r}}_{\mathrm{e}}}=\sqrt{2\times \frac{121\mathrm{h}}{100}\times {\mathrm{r}}_{\mathrm{e}}}=\frac{11}{10}\sqrt{2{\mathrm{hr}}_{\mathrm{e}}}=\frac{11}{10}\times \mathrm{d}=\frac{110}{100}\times \mathrm{d}$

$\Rightarrow \frac{{\mathrm{d}}^1-\mathrm{d}}{\mathrm{d}}=\frac{10}{100}$

$\therefore \%$change in transmission range is 10%