Question Number 133722 by I want to learn more last updated on 23/Feb/21
Answered by mr W last updated on 23/Feb/21
$${x}=\mathrm{28}\left(\mathrm{tan}\:\mathrm{40}−\mathrm{tan}\:\mathrm{20}\right) \\ $$
Answered by bramlexs22 last updated on 23/Feb/21
$$\mathrm{tan}\:\mathrm{40}°=\frac{\mathrm{CB}}{\mathrm{28}}...\left(\mathrm{i}\right) \\ $$$$\mathrm{tan}\:\mathrm{20}°\:=\:\frac{\mathrm{BD}}{\mathrm{28}}...\left(\mathrm{ii}\right) \\ $$$$\mathrm{CB}\:=\:{x}\:+\:\mathrm{BD}...\left(\mathrm{iii}\right) \\ $$$$\Leftrightarrow\:{x}\:+\mathrm{28}\:\mathrm{tan}\:\mathrm{20}°\:=\:\mathrm{28}\:\mathrm{tan}\:\mathrm{40}° \\ $$$$\Leftrightarrow\:{x}\:=\:\mathrm{28}\:\left\{\:\frac{\mathrm{2tan}\:\mathrm{20}°}{\mathrm{1}−\mathrm{tan}\:^{\mathrm{2}} \mathrm{20}°}\:−\:\mathrm{tan}\:\mathrm{20}°\:\right\} \\ $$