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Category: Geometry

Question-177205

Question Number 177205 by HeferH last updated on 02/Oct/22 Answered by mr W last updated on 02/Oct/22 $$\angle{CAD}=\mathrm{180}−\mathrm{120}−\mathrm{3}{x}=\mathrm{60}−\mathrm{3}{x} \\ $$$$\angle{CDB}=\mathrm{180}−\mathrm{3}{x} \\ $$$${applying}\:{law}\:{of}\:{sines}: \\ $$$$\frac{\mathrm{sin}\:\left(\mathrm{60}−\mathrm{3}{x}\right)}{{CD}}=\frac{\mathrm{sin}\:\mathrm{120}}{{AD}}\:\:\:…\left({i}\right) \\…

Question-46073

Question Number 46073 by ajfour last updated on 20/Oct/18 Commented by ajfour last updated on 20/Oct/18 $${Determine}\:{coordinates}\:{of}\:{A}; \\ $$$$\:\:\:{b}\:>\:{c}\:.\:{P}\:{is}\:{contact}\:{point}\:{of}\:{side} \\ $$$${AB}\:{of}\:\bigtriangleup{ABC}\:{with}\:{upper}\:{rim}\:{of} \\ $$$${cylinder}\:\left({height}\:{H},\:{radius}\:{R}\right). \\ $$…

In-a-trapezoid-ABCD-sides-AB-and-CD-are-parallel-and-side-BC-CD-5-If-DC-B-120-and-BA-D-60-Find-the-area-of-ABCD-

Question Number 111539 by Aina Samuel Temidayo last updated on 04/Sep/20 $$\mathrm{In}\:\mathrm{a}\:\mathrm{trapezoid}\:\mathrm{ABCD},\:\mathrm{sides}\:\mathrm{AB}\:\mathrm{and} \\ $$$$\mathrm{CD}\:\mathrm{are}\:\mathrm{parallel}\:\mathrm{and}\:\mathrm{side}\:\mathrm{BC}=\mathrm{CD}=\sqrt{\mathrm{5}}. \\ $$$$\mathrm{If}\:\mathrm{D}\hat {\mathrm{C}B}\:=\mathrm{120}°\:\mathrm{and}\:\mathrm{B}\hat {\mathrm{A}D}=\mathrm{60}°.\:\mathrm{Find} \\ $$$$\mathrm{the}\:\mathrm{area}\:\mathrm{of}\:\mathrm{ABCD}. \\ $$ Answered by 1549442205PVT…

Question-45980

Question Number 45980 by ajfour last updated on 19/Oct/18 Commented by ajfour last updated on 19/Oct/18 $${Determine}\:{sides}\:{of}\:\bigtriangleup,\: \\ $$$$\boldsymbol{{a}},\:{and}\:\boldsymbol{{b}}\:=\:\boldsymbol{{c}}\:,\:{in}\:{terms}\:{of}\:\boldsymbol{{R}},\:\boldsymbol{{r}},\:\boldsymbol{{d}}. \\ $$ Answered by MrW3 last…

Question-111497

Question Number 111497 by bemath last updated on 04/Sep/20 Commented by kaivan.ahmadi last updated on 04/Sep/20 $${let}\:{t}={x}_{\mathrm{1}} ^{\mathrm{3}} +\mathrm{6}{x}_{\mathrm{1}} ^{\mathrm{2}} −\mathrm{30}{x}_{\mathrm{1}} +{x}_{\mathrm{1}} ^{\mathrm{2}} {x}_{\mathrm{2}} −\mathrm{5}{x}_{\mathrm{1}}…

Triangle-ABC-has-AB-2-AC-Let-D-and-E-be-on-AB-and-BC-respectively-such-that-BAE-ACD-Let-F-be-the-intersections-of-segments-AE-and-CD-and-suppose-that-CFE-is-equilateral-What-is-ACB-

Question Number 111477 by Aina Samuel Temidayo last updated on 03/Sep/20 $$\mathrm{Triangle}\:\mathrm{ABC}\:\mathrm{has}\:\mathrm{AB}=\mathrm{2}\centerdot\mathrm{AC}.\:\mathrm{Let} \\ $$$$\mathrm{D}\:\mathrm{and}\:\mathrm{E}\:\mathrm{be}\:\mathrm{on}\:\mathrm{AB}\:\mathrm{and}\:\mathrm{BC} \\ $$$$\mathrm{respectively}\:\mathrm{such}\:\mathrm{that}\:\angle\mathrm{BAE} \\ $$$$=\angle\mathrm{ACD}.\:\mathrm{Let}\:\mathrm{F}\:\mathrm{be}\:\mathrm{the}\:\mathrm{intersections}\:\mathrm{of} \\ $$$$\mathrm{segments}\:\mathrm{AE}\:\mathrm{and}\:\mathrm{CD},\:\mathrm{and}\:\mathrm{suppose} \\ $$$$\mathrm{that}\:\bigtriangleup\mathrm{CFE}\:\mathrm{is}\:\mathrm{equilateral}.\:\mathrm{What}\:\mathrm{is} \\ $$$$\angle\mathrm{ACB}? \\…