Question-185602

Question Number 185602 by Mingma last updated on 24/Jan/23

Answered by mr W last updated on 24/Jan/23

say AB=DE=1 BD=DC=(1/(2 sin 20°)) (1/(2 sin 20° sin (α+20°)))=(1/(sin 20°)) sin (α+20°)=(1/2) α+20°=150° ⇒α=130°

$${say}\:{AB}={DE}=\mathrm{1} \\ $$$${BD}={DC}=\frac{\mathrm{1}}{\mathrm{2}\:\mathrm{sin}\:\mathrm{20}°} \\ $$$$\frac{\mathrm{1}}{\mathrm{2}\:\mathrm{sin}\:\mathrm{20}°\:\mathrm{sin}\:\left(\alpha+\mathrm{20}°\right)}=\frac{\mathrm{1}}{\mathrm{sin}\:\mathrm{20}°} \\ $$$$\mathrm{sin}\:\left(\alpha+\mathrm{20}°\right)=\frac{\mathrm{1}}{\mathrm{2}} \\ $$$$\alpha+\mathrm{20}°=\mathrm{150}° \\ $$$$\Rightarrow\alpha=\mathrm{130}° \\ $$

Commented by malwan last updated on 24/Jan/23