Question and Answers Forum

All Questions      Topic List

Geometry Questions

Previous in All Question      Next in All Question      

Previous in Geometry      Next in Geometry      

Question Number 193958 by Rupesh123 last updated on 24/Jun/23

Answered by ARUNG_Brandon_MBU last updated on 24/Jun/23

$$\frac{a}{\sin (150°-x)}=\frac{b}{\sin 30°}=2b$$$$\frac{a}{\sin 30°}=\frac{a+b}{\sin (150°-x)}=2a$$$$\Rightarrow 2b(a+b)=2a^2\Rightarrow a^2-ab-b^2=0$$$$\Rightarrow {\left(\frac{a}{b}\right)}^2-\frac{a}{b}-1=0\Rightarrow \frac{a}{b}=\frac{1\pm \sqrt{5}}{2}$$$$\Rightarrow \sin (150°-x)=\frac{a}{2b}=\frac{1\pm \sqrt{5}}{4}$$$$\Rightarrow \sin (x+30°)=\frac{1\pm \sqrt{5}}{4}$$$$\Rightarrow x=\arcsin \left(\frac{1\pm \sqrt{5}}{4}\right)-30°,x>0$$$$\Rightarrow x=\arcsin \left(\frac{1+\sqrt{5}}{4}\right)-30°=24°$$

Commented by Rupesh123 last updated on 25/Jun/23

Perfect

Terms of Service

Privacy Policy

Contact: info@tinkutara.com