Question Number 51088 by ajfour last updated on 23/Dec/18 Commented by ajfour last updated on 23/Dec/18 $${Find}\:{maximum}\:{area}\:{of}\:\bigtriangleup{ABC}. \\ $$ Answered by ajfour last updated on…
Question Number 182155 by Acem last updated on 05/Dec/22 Commented by Acem last updated on 05/Dec/22 $$\:{Find}\:{the}\:{length}\:{of}\:{the}\:{crease}\:{L}\left({w},\:\theta\right) \\ $$$$\:{Q}.\mathrm{181128} \\ $$ Answered by Acem last…
Question Number 182149 by Acem last updated on 05/Dec/22 Commented by Acem last updated on 05/Dec/22 $$\:{Find}\:\alpha \\ $$ Answered by HeferH last updated on…
Question Number 182135 by Acem last updated on 04/Dec/22 Commented by Acem last updated on 04/Dec/22 $${Sum}\:{of}\:{their}\:{areas}\:\uparrow \\ $$ Answered by mr W last updated…
Question Number 182103 by mr W last updated on 04/Dec/22 Commented by mr W last updated on 04/Dec/22 $${find}\:{the}\:{smallest}\:{area}\:{of}\:{inscribed}\: \\ $$$${equilateral}\:{triangle}\:{in}\:{the}\:{given}\: \\ $$$${triangle}\:{with}\:{sides}\:\mathrm{3},\mathrm{5},\mathrm{7}. \\ $$…
Question Number 182091 by mr W last updated on 04/Dec/22 Commented by mr W last updated on 04/Dec/22 $${the}\:{areas}\:{of}\:{three}\:{squares}\:{are}\:{given}. \\ $$$${find}\:{the}\:{sum}\:{of}\:{the}\:{areas}\:{of}\:{the}\:{other} \\ $$$${four}\:{squares}. \\ $$…
Question Number 182078 by Acem last updated on 04/Dec/22 Answered by mr W last updated on 05/Dec/22 $$\frac{\mathrm{sin}\:\mathrm{30}}{\mathrm{sin}\:\left(\mathrm{30}−\theta\right)}=\frac{\mathrm{sin}\:\left(\mathrm{30}+\theta\right)}{\mathrm{sin}\:\theta} \\ $$$$\frac{\mathrm{sin}\:\theta}{\mathrm{2}}=\frac{\left(\mathrm{cos}\:\theta+\sqrt{\mathrm{3}}\:\mathrm{sin}\:\theta\right)\left(\mathrm{cos}\:\theta−\sqrt{\mathrm{3}}\:\mathrm{sin}\:\theta\right)}{\mathrm{4}} \\ $$$$\mathrm{2}\:\mathrm{sin}\:\theta=\mathrm{cos}^{\mathrm{2}} \:\theta−\mathrm{3}\:\mathrm{sin}^{\mathrm{2}} \:\theta \\…
Question Number 182075 by Acem last updated on 04/Dec/22 Commented by Acem last updated on 04/Dec/22 $${Regular}\:{hexagon}\:\uparrow \\ $$ Answered by mr W last updated…
Question Number 182066 by HeferH last updated on 03/Dec/22 Answered by a.lgnaoui last updated on 04/Dec/22 $$\bigtriangleup\mathrm{ABC}\:\: \\ $$$$\mathrm{ABcos}\:\mathrm{2x}+\mathrm{BCcos}\:\mathrm{x}=\mathrm{ADcos}\:\mathrm{3x}+\mathrm{CDcos}\:\mathrm{4x} \\ $$$$\frac{\mathrm{sin}\:\mathrm{2x}}{\mathrm{BC}}=\frac{\mathrm{sinx}\:}{\mathrm{AB}}\:\:\:\left(\mathrm{1}\right)\:\:\:\:\:\:\:\frac{\mathrm{sin}\:\mathrm{3x}}{\mathrm{CD}}\:\:\:\:=\frac{\mathrm{sin}\:\mathrm{4x}}{\mathrm{AD}}\left(\mathrm{2}\right) \\ $$$$\mathrm{ABsin}\:\mathrm{2x}=\mathrm{BCsin}\:\mathrm{x}\:\:\:\:\:\mathrm{AD}\:\mathrm{sin}\:\mathrm{3x}=\mathrm{CDsin}\:\mathrm{4x} \\ $$$$\mathrm{AB}=\frac{\mathrm{BCsin}\:\mathrm{x}}{\mathrm{sin}\:\mathrm{2x}}\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{CD}=\frac{\mathrm{ADsin}\:\mathrm{3x}}{\mathrm{sin}\:\mathrm{4x}}…
Question Number 182006 by mr W last updated on 03/Dec/22 Commented by mr W last updated on 03/Dec/22 $${find}\:{the}\:{largest}\:{area}\:{of}\:{an}\:{inscribed} \\ $$$${right}−{angle}\:{triangle}\:{in}\:{a}\:{given}\:{acute} \\ $$$${triangle}\:{with}\:{sides}\:{a},{b},{c}.\:\left({a}\geqslant{b}\geqslant{c}\right) \\ $$…