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Category: Geometry

Question-194056

Question Number 194056 by ajfour last updated on 26/Jun/23 Answered by a.lgnaoui last updated on 27/Jun/23 $$\mathrm{ABC}\:\:\:\mathrm{triangle}\:\mathrm{equilaterale}\:\: \\ $$$$\mathrm{AB}=\mathrm{BC}=\mathrm{AC}\:\:\:\mathrm{BC}=\mathrm{2acos}\:\mathrm{30}=\mathrm{a}\sqrt{\mathrm{3}} \\ $$$$\Rightarrow\mathrm{AH}=\mathrm{BCsin}\:\mathrm{60}=\frac{\mathrm{3a}}{\mathrm{2}} \\ $$$$\:\:\mathrm{AI}=\mathrm{AM}+\mathrm{MI}=\mathrm{2a}\:\:\:\:\:\left(\mathrm{i}\right) \\ $$$$\:\:\measuredangle\mathrm{MAN}=\mathrm{30}\:;\mathrm{sin}\:\mathrm{30}=\frac{\mathrm{c}}{\mathrm{AM}}\Rightarrow\:\mathrm{AM}=\mathrm{2}\boldsymbol{\mathrm{c}}…

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}}…