Question Number 224672 by wongb1506 last updated on 25/Sep/25
Answered by mr W last updated on 26/Sep/25
Commented by mr W last updated on 26/Sep/25
$${X}=\mathrm{108}° \\ $$$$\mathrm{sin}\:{X}=\mathrm{sin}\:\mathrm{108}°=\mathrm{sin}\:\mathrm{72}° \\ $$$$\:\:\:\:\:\:\:\:\:\:\:=\sqrt{\mathrm{1}−\left(\frac{\sqrt{\mathrm{5}}−\mathrm{1}}{\mathrm{4}}\right)^{\mathrm{2}} }=\frac{\sqrt{\mathrm{2}\left(\mathrm{5}+\sqrt{\mathrm{5}}\right)}}{\mathrm{4}} \\ $$
Commented by mr W last updated on 26/Sep/25
$$\mathrm{cos}\:\mathrm{72}°=\mathrm{sin}\:\mathrm{18}°=\frac{\sqrt{\mathrm{5}}−\mathrm{1}}{\mathrm{4}} \\ $$