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 90011 by I want to learn more last updated on 20/Apr/20

Commented by mr W last updated on 21/Apr/20

$$x\sin \frac{a}{2}=\frac{x^2}{2}$$$$\sin \frac{a}{2}=\frac{x}{2}$$$$\sin \frac{3a}{2}=3\left(\frac{x}{2}\right)-4{\left(\frac{x}{2}\right)}^3=\frac{1}{2}(3x-x^3)=\frac{\sqrt{3}}{2}$$$$\frac{3a}{2}=60°or120°$$$$\Rightarrow a=40°or80°$$

Commented by I want to learn more last updated on 20/Apr/20

$$\mathrm{Thanks}\mathrm{sir}.\mathrm{I}\mathrm{appreciate}.$$

Commented by MJS last updated on 21/Apr/20

$$\mathrm{is}a=80°\mathrm{also}\mathrm{possible}?$$$$x^3-3x+\sqrt{3}=0$$$$x_1=2\sin \frac{\pi }{9}\Rightarrow a=40°$$$$x_2=2\sin \frac{2\pi }{9}\Rightarrow a=80°$$$$x_3=-2\cos \frac{\pi }{18}\left[\mathrm{impossible}\right]$$

Commented by john santu last updated on 21/Apr/20

$$\sin \left(\frac{3a}{2}\right)=\sin {120}^o$$$$\frac{3a}{2}={120}^o\Rightarrow a={80}^o$$$$solution\{{40}^o,{80}^o\}$$

Commented by mr W last updated on 21/Apr/20

$$yes.$$

Commented by I want to learn more last updated on 21/Apr/20

$$\mathrm{Thanks}\mathrm{sirs}$$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com