Menu Close

Category: Geometry

Question-49536

Question Number 49536 by behi83417@gmail.com last updated on 07/Dec/18 Commented by behi83417@gmail.com last updated on 07/Dec/18 $$\bigtriangleup\:{and}\bigtriangleup\:{are}\:{equilateral}\:{triangles}\:{with} \\ $$$${parallel}\:{sides}\:{and}\:\boldsymbol{\mathrm{PM}},{is}\:{the}\:{same}\:{for} \\ $$$${all}\:{sides}.{if}:{area}\left(\bigtriangleup\right)=\mathrm{32}\:{and}\:{area}\left(\bigtriangleup\right)=\mathrm{6}, \\ $$$${then}:{valve}\:{of}\::\boldsymbol{\mathrm{PM}}=? \\ $$…

Question-49530

Question Number 49530 by behi83417@gmail.com last updated on 07/Dec/18 Commented by behi83417@gmail.com last updated on 07/Dec/18 $$\bigtriangleup\:{and}\:\bigtriangleup\:{are}\:{equilateral}\:{triangles}. \\ $$$${AB}=\mathrm{4},{EG}=\mathrm{2}\sqrt{\mathrm{2}}\:\:\:\left[{or}:{AB}=\mathrm{6},{EG}=\mathrm{2}\sqrt{\mathrm{6}}\right] \\ $$$$\Rightarrow\:\:\:\:\:{AE}=?\:\:\:\:,\:\:\:\:\:\measuredangle{AEI}=? \\ $$ Commented by…

Question-49430

Question Number 49430 by behi83417@gmail.com last updated on 06/Dec/18 Commented by behi83417@gmail.com last updated on 07/Dec/18 $${D}\overset{} {{A}E}=\boldsymbol{\theta},{AD}=\boldsymbol{{r}}\:\:\:. \\ $$$${there}\:{is}\:{two}\:{equilateral}\:{triangles}, \\ $$$$\:{inscribed}\:{in}\:{circle}\:,{one}\:{vertex}\:{on}\: \\ $$$${point}:{C}\:{and}\:{two}\:{anothers}\:{locate}\:{on} \\…

Question-180459

Question Number 180459 by mnjuly1970 last updated on 12/Nov/22 Answered by greougoury555 last updated on 12/Nov/22 $$\:\:\mathrm{cos}\:\mathrm{3}\alpha=\frac{\mathrm{1}}{\mathrm{2cos}\:\alpha} \\ $$$$\:\:\mathrm{4cos}\:^{\mathrm{3}} \alpha−\mathrm{3cos}\:\alpha=\frac{\mathrm{1}}{\mathrm{2cos}\:\alpha} \\ $$$$\:\:\mathrm{cos}\:\alpha=\:\frac{\sqrt{\mathrm{6}+\mathrm{2}\sqrt{\mathrm{17}}}}{\mathrm{4}}\: \\ $$$$\:\mathrm{sin}\:\alpha\:=\:\frac{\sqrt{\mathrm{10}−\mathrm{2}\sqrt{\mathrm{17}}}}{\mathrm{4}} \\…

Question-49384

Question Number 49384 by Pk1167156@gmail.com last updated on 06/Dec/18 Commented by Kunal12588 last updated on 06/Dec/18 $${for}\:\bigtriangleup{ABD} \\ $$$${AD}=\mathrm{39} \\ $$$${pythagorean}\:{triples}\:{with}\:{side}\:\mathrm{39} \\ $$$$\mathrm{1}.\:\mathrm{39},\mathrm{52},\mathrm{65}\:\:\:\:\:\:\:\:\:\:\:× \\ $$$$\mathrm{2}.\mathrm{39},\mathrm{80},\mathrm{89}\:\:\:…

Question-180458

Question Number 180458 by mnjuly1970 last updated on 12/Nov/22 Answered by mr W last updated on 13/Nov/22 $${c}^{\mathrm{2}} =\mathrm{1}^{\mathrm{2}} +\left(\sqrt{\mathrm{3}}\right)^{\mathrm{2}} +\mathrm{2}×\mathrm{1}×\sqrt{\mathrm{3}}×\frac{\mathrm{1}}{\mathrm{2}}=\mathrm{4}+\sqrt{\mathrm{3}} \\ $$$$\frac{\mathrm{sin}\:\alpha}{\:\sqrt{\mathrm{3}}}=\frac{\mathrm{sin}\:\mathrm{120}°}{\:\sqrt{\mathrm{4}+\sqrt{\mathrm{3}}}} \\ $$$$\mathrm{sin}\:\alpha=\sqrt{\mathrm{3}}×\frac{\sqrt{\mathrm{3}}}{\mathrm{2}}×\frac{\mathrm{1}}{\:\sqrt{\mathrm{4}+\sqrt{\mathrm{3}}}}=\frac{\mathrm{3}}{\mathrm{2}\sqrt{\mathrm{4}+\sqrt{\mathrm{3}}}}…