Question Number 123784 by help last updated on 28/Nov/20
Answered by mr W last updated on 28/Nov/20
Commented by mr W last updated on 28/Nov/20
$${let}\:{AB}=\mathrm{1} \\ $$$${BD}=\frac{{AB}}{\mathrm{tan}\:\mathrm{40}°}=\frac{\mathrm{1}}{\mathrm{tan}\:\mathrm{40}°} \\ $$$${BC}=\frac{{BD}}{\mathrm{tan}\:\mathrm{20}°}=\frac{\mathrm{1}}{\mathrm{tan}\:\mathrm{20}°\:\mathrm{tan}\:\mathrm{40}°} \\ $$$${BE}={BC}×\mathrm{tan}\:\mathrm{10}°=\frac{\mathrm{tan}\:\mathrm{10}°}{\mathrm{tan}\:\mathrm{20}°\:\mathrm{tan}\:\mathrm{40}°} \\ $$$$\mathrm{tan}\:{x}=\frac{{BE}}{{AB}}=\frac{\mathrm{tan}\:\mathrm{10}°}{\mathrm{tan}\:\mathrm{20}°\:\mathrm{tan}\:\mathrm{40}°}=\mathrm{tan}\:\mathrm{30}° \\ $$$$\Rightarrow{x}=\mathrm{30}° \\ $$