Menu Close

Category: Geometry

Question-186298

Question Number 186298 by TUN last updated on 03/Feb/23 Answered by a.lgnaoui last updated on 05/Feb/23 $$\bigtriangleup{ABC}\:\::\:\mathrm{6}+\mathrm{36}+{x}+{y}+\mathrm{z}+\mathrm{12}=\mathrm{180} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{x}+{y}+\mathrm{z}=\mathrm{126} \\ $$$$\:\bigtriangleup\mathrm{ACD}:\:\:\frac{\mathrm{sin}\:{x}}{\mathrm{AD}}=\frac{\mathrm{sin}\:\mathrm{y}}{\mathrm{CD}}=\frac{\mathrm{sin}\:\left(\mathrm{x}+\mathrm{y}\right)}{\mathrm{AC}}\left(\mathrm{1}\right) \\ $$$$\bigtriangleup\mathrm{ABC}\:\:\:\frac{\mathrm{sin}\:\left(\mathrm{y}+\mathrm{12}\right)}{\mathrm{BC}}=\frac{\mathrm{sin}\:\mathrm{42}}{\mathrm{AC}}\left(\mathrm{2}\right) \\ $$$$\:\left(\mathrm{1}\right)\Rightarrow\mathrm{sin}\:{y}=\frac{{CD}}{{AD}}\mathrm{sin}\:\mathrm{x}…

Question-186271

Question Number 186271 by cherokeesay last updated on 02/Feb/23 Answered by HeferH last updated on 02/Feb/23 Commented by HeferH last updated on 02/Feb/23 $${x}\:+\:\frac{{x}}{\:\sqrt{\mathrm{3}}}\:+\:\frac{\mathrm{2}}{\:\sqrt{\mathrm{3}}}\left({x}\:+\:{x}\sqrt{\mathrm{3}}\right)\:=\:\mathrm{6} \\…

Question-186165

Question Number 186165 by ajfour last updated on 01/Feb/23 Answered by mr W last updated on 01/Feb/23 $$\frac{{c}}{{x}}=\frac{{x}−\mathrm{1}}{\:\sqrt{{x}^{\mathrm{2}} −\left({x}−\mathrm{1}\right)^{\mathrm{2}} }}=\frac{{x}−\mathrm{1}}{\:\sqrt{\mathrm{2}{x}−\mathrm{1}}} \\ $$$${x}\left({x}−\mathrm{1}\right)={c}\sqrt{\mathrm{2}{x}−\mathrm{1}} \\ $$$${x}^{\mathrm{4}} −\mathrm{2}{x}^{\mathrm{3}}…