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Question Number 160325 by NUR23 last updated on 27/Nov/21

Commented by NUR23 last updated on 27/Nov/21

$$Bythenameofodinplzhelpme$$$$$$

Commented by mr W last updated on 29/Nov/21

$$yesterdayisawamancryingloudly$$$$forhelponthestreet.thenpeople$$$$cameandhelpedihm.whatdidthe$$$$man?nothing!hespokenowordas$$$$ifheweredump.heneitherthanked$$$$thepeoplewhohelpedhimnortoldif$$$$theproblemhehadwasgone.iguess$$$$nexttimewhenhecriesforhelp$$$$again,notsomanypeoplewillcome$$$$tohelphim.$$

Commented by Tawa11 last updated on 03/Dec/21

$$\mathrm{That}\mathrm{is}\mathrm{human}\mathrm{being}\mathrm{sir}.$$$$\mathrm{I}\mathrm{personally}\mathrm{love}\mathrm{your}\mathrm{geometry}\mathrm{solutions}\mathrm{sir}.$$$$\mathrm{That}\mathrm{is}\mathrm{why}\mathrm{I}\mathrm{follow}\mathrm{your}\mathrm{solutions}\mathrm{everytime}.$$$$\mathrm{God}\mathrm{bless}\mathrm{you}\mathrm{sir}.$$

Answered by mr W last updated on 27/Nov/21

$$sayOE=1$$$$\frac{OF}{\sin 40}=\frac{EF}{\sin 60}=\frac{OE}{\sin 100}$$$$OF=\frac{\sin 40}{\sin 100}$$$$EF=\frac{\sin 60}{\sin 100}$$$$\frac{OU}{\sin 35}=\frac{EU}{\sin 80}=\frac{OE}{\sin 115}$$$$OU=\frac{\sin 35}{\sin 115}$$$$EU=\frac{\sin 80}{\sin 115}$$$$UF=\sqrt{{\left(\frac{\sin 80}{\sin 115}\right)}^2+{\left(\frac{\sin 60}{\sin 100}\right)}^2-2\left(\frac{\sin 80}{\sin 115}\right)\left(\frac{\sin 60}{\sin 100}\right)\cos 5}$$$$\frac{\sin x}{OU}=\frac{\sin 20}{UF}$$$$\sin x=\frac{OU\times \sin 20}{UF}$$$$=\frac{\sin 35\times \sin 20}{\sin 115\times \sqrt{{\left(\frac{\sin 80}{\sin 115}\right)}^2+{\left(\frac{\sin 60}{\sin 100}\right)}^2-2\left(\frac{\sin 80}{\sin 115}\right)\left(\frac{\sin 60}{\sin 100}\right)\cos 5}}$$$$x={\sin }^{-1}\frac{\sin 35\times \sin 20}{\sin 115\times \sqrt{{\left(\frac{\sin 80}{\sin 115}\right)}^2+{\left(\frac{\sin 60}{\sin 100}\right)}^2-2\left(\frac{\sin 80}{\sin 115}\right)\left(\frac{\sin 60}{\sin 100}\right)\cos 5}}$$$$=75°$$

Commented by Tawa11 last updated on 28/Nov/21

$$\mathrm{Great}\mathrm{sir}.$$

Commented by NUR23 last updated on 08/Mar/22

$$thankyouverymuchsiriwasoutlfthe?line$$

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