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Category: Coordinate Geometry

calcul-de-l-angle-x-ABD-sin-y-AD-sin44-BD-1-ADC-sin-x-AD-sin48-DC-2-1-BD-sin-y-ADsin-44-2-DCsinx-ADsin-48-1-2-BDsin-y-DCsin-x-

Question Number 185169 by a.lgnaoui last updated on 18/Jan/23 $${calcul}\:{de}\:{l}'\:{angle}\:\boldsymbol{{x}} \\ $$$$\bigtriangleup{ABD}\:\:\:\:\:\frac{\mathrm{sin}\:\mathrm{y}}{\mathrm{AD}}=\frac{\mathrm{sin44}\:}{\mathrm{BD}}\:\:\left(\mathrm{1}\right) \\ $$$$\bigtriangleup{ADC}\:\:\:\:\:\frac{\mathrm{sin}\:\mathrm{x}}{\mathrm{AD}}=\frac{\mathrm{sin48}\:}{\mathrm{DC}}\:\left(\mathrm{2}\right) \\ $$$$\left(\mathrm{1}\right)\:\:\:\:\:\mathrm{BD}\:\mathrm{sin}\:\mathrm{y}=\mathrm{ADsin}\:\mathrm{44} \\ $$$$\left(\mathrm{2}\right)\:\:\:\:\:\:\mathrm{DCsinx}\:=\mathrm{ADsin}\:\mathrm{48} \\ $$$$ \\ $$$$\frac{\left(\mathrm{1}\right)}{\left(\mathrm{2}\right)}\Leftrightarrow\:\frac{\mathrm{BDsin}\:\mathrm{y}}{\mathrm{DCsin}\:\mathrm{x}}=\frac{\mathrm{sin}\:\mathrm{44}}{\mathrm{sin}\:\mathrm{48}}\:\:\:\left(\mathrm{3}\right) \\ $$$$ \\…

Question-54068

Question Number 54068 by ajfour last updated on 28/Jan/19 Commented by ajfour last updated on 28/Jan/19 $${locate}\:{P}\:\left({x},{y}\right)\:{such}\:{that}\:\bigtriangleup{APB}, \\ $$$$\bigtriangleup{BPC},\:{and}\:\bigtriangleup{CPA}\:{each}\:{have}\:{the} \\ $$$${same}\:{perimeter}.\:\left({in}\:{terms}\:{of}\:{a},{b},{c}\right) \\ $$ Commented by…

The-points-A-B-C-D-have-coordinates-7-9-3-4-1-12-and-2-9-find-the-length-of-the-linePQ-where-P-devides-AB-in-the-ratio-2-3-and-devides-CD-in-the-ratio-1-4-

Question Number 54025 by pieroo last updated on 28/Jan/19 $$\mathrm{The}\:\mathrm{points}\:\mathrm{A},\:\mathrm{B},\:\mathrm{C},\:\mathrm{D}\:\mathrm{have}\:\mathrm{coordinates} \\ $$$$\left(−\mathrm{7},\mathrm{9}\right),\:\left(\mathrm{3},\mathrm{4}\right),\:\left(\mathrm{1},\mathrm{12}\right),\:\mathrm{and}\:\left(−\mathrm{2},−\mathrm{9}\right). \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{length}\:\mathrm{of}\:\mathrm{the}\:\mathrm{linePQ}\:\mathrm{where}\:\mathrm{P} \\ $$$$\mathrm{devides}\:\mathrm{AB}\:\mathrm{in}\:\mathrm{the}\:\mathrm{ratio}\:\mathrm{2}:\mathrm{3}\:\mathrm{and}\:\mathrm{devides} \\ $$$$\mathrm{CD}\:\mathrm{in}\:\mathrm{the}\:\mathrm{ratio}\:\mathrm{1}:−\mathrm{4}. \\ $$ Commented by pieroo last updated…