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Category: Geometry

Question-193958

Question Number 193958 by Rupesh123 last updated on 24/Jun/23 Answered by ARUNG_Brandon_MBU last updated on 24/Jun/23 $$\frac{{a}}{\mathrm{sin}\left(\mathrm{150}°−{x}\right)}=\frac{{b}}{\mathrm{sin30}°}=\mathrm{2}{b} \\ $$$$\frac{{a}}{\mathrm{sin30}°}=\frac{{a}+{b}}{\mathrm{sin}\left(\mathrm{150}°−{x}\right)}=\mathrm{2}{a} \\ $$$$\Rightarrow\mathrm{2}{b}\left({a}+{b}\right)=\mathrm{2}{a}^{\mathrm{2}} \:\Rightarrow{a}^{\mathrm{2}} −{ab}−{b}^{\mathrm{2}} =\mathrm{0} \\…

Question-193906

Question Number 193906 by cherokeesay last updated on 22/Jun/23 Answered by Subhi last updated on 22/Jun/23 $$ \\ $$$$\frac{\mathrm{1}}{{sin}\left(\mathrm{18}\right)}=\frac{\mathrm{1}+{y}}{{sin}\left(\mathrm{144}−{x}\right)}\: \\ $$$$\frac{\mathrm{1}}{{sin}\left(\mathrm{18}\right)}=\frac{{y}}{{sin}\left({x}\right)}\:\Rrightarrow\:{y}\:=\:\frac{{sin}\left({x}\right)}{{sin}\left(\mathrm{18}\right)} \\ $$$$\frac{\mathrm{1}}{{sin}\left(\mathrm{18}\right)}=\frac{\mathrm{1}+\frac{{sin}\left({x}\right)}{{sin}\left(\mathrm{18}\right)}}{{sin}\left(\mathrm{144}−{x}\right)} \\ $$$${sin}\left(\mathrm{144}−{x}\right)={sin}\left(\mathrm{18}\right)+{sin}\left({x}\right)…

Question-193726

Question Number 193726 by mr W last updated on 18/Jun/23 Answered by som(math1967) last updated on 18/Jun/23 $${a}+{b}+{c} \\ $$$$=\mathrm{tan}^{−\mathrm{1}} \frac{\mathrm{1}}{\mathrm{3}}\:+\mathrm{tan}^{−\mathrm{1}} \frac{\mathrm{1}}{\mathrm{2}}+\mathrm{tan}^{−\mathrm{1}} \mathrm{1} \\ $$$$=\mathrm{tan}^{−\mathrm{1}}…

Question-193635

Question Number 193635 by mr W last updated on 17/Jun/23 Commented by mr W last updated on 17/Jun/23 $${find}\:{the}\:{largest}\:{circle}\:{and}\:{the}\:{largest} \\ $$$${square}\:{which}\:{you}\:{can}\:{completely} \\ $$$${cover}\:{with}\:{three}\:{circular}\:{plates}\:{with} \\ $$$${radius}\:\mathrm{1}\:{respectively}.…