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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=1  BD=((AB)/(tan 40°))=(1/(tan 40°))  BC=((BD)/(tan 20°))=(1/(tan 20° tan 40°))  BE=BC×tan 10°=((tan 10°)/(tan 20° tan 40°))  tan x=((BE)/(AB))=((tan 10°)/(tan 20° tan 40°))=tan 30°  ⇒x=30°

$${let}\:{AB}=\mathrm{1} \\ $$$${BD}=\frac{{AB}}{\mathrm{tan}\:\mathrm{40}°}=\frac{\mathrm{1}}{\mathrm{tan}\:\mathrm{40}°} \\ $$$${BC}=\frac{{BD}}{\mathrm{tan}\:\mathrm{20}°}=\frac{\mathrm{1}}{\mathrm{tan}\:\mathrm{20}°\:\mathrm{tan}\:\mathrm{40}°} \\ $$$${BE}={BC}×\mathrm{tan}\:\mathrm{10}°=\frac{\mathrm{tan}\:\mathrm{10}°}{\mathrm{tan}\:\mathrm{20}°\:\mathrm{tan}\:\mathrm{40}°} \\ $$$$\mathrm{tan}\:{x}=\frac{{BE}}{{AB}}=\frac{\mathrm{tan}\:\mathrm{10}°}{\mathrm{tan}\:\mathrm{20}°\:\mathrm{tan}\:\mathrm{40}°}=\mathrm{tan}\:\mathrm{30}° \\ $$$$\Rightarrow{x}=\mathrm{30}° \\ $$

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