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Category: Geometry

Question-186557

Question Number 186557 by Mingma last updated on 06/Feb/23 Answered by mr W last updated on 06/Feb/23 $${h}={height}\:{of}\:{trapezoid} \\ $$$${area}\:{of}\:{trapezoid}\:=\frac{\left(\mathrm{5}+\mathrm{6}\right){h}}{\mathrm{2}} \\ $$$${area}\:{of}\:{triangle}\:{with}\:{base}\:{b}=\frac{{bh}}{\mathrm{2}} \\ $$$${which}\:{is}\:{a}\:{third}\:{of}\:{the}\:{total}\:{area}, \\…

Question-186549

Question Number 186549 by Mingma last updated on 05/Feb/23 Answered by mr W last updated on 06/Feb/23 $${say}\:{AD}={AC}={CE}={a} \\ $$$${AE}=\mathrm{2}{a}\:\mathrm{cos}\:\mathrm{70}° \\ $$$${DE}^{\mathrm{2}} ={a}^{\mathrm{2}} +\left(\mathrm{2}{a}\:\mathrm{cos}\:\mathrm{70}\right)^{\mathrm{2}} −\mathrm{2}{a}×\mathrm{2}{a}\:\mathrm{cos}\:\mathrm{70}×\mathrm{cos}\:\mathrm{50}…

Question-186551

Question Number 186551 by ajfour last updated on 05/Feb/23 Commented by mr W last updated on 06/Feb/23 $${square}\:{with}\:{side}\:{length}\:\mathrm{1}? \\ $$$${A}_{{shade}} =\frac{{t}^{\mathrm{2}} \left({t}+\mathrm{2}\right)^{\mathrm{2}} }{\mathrm{4}\left(\mathrm{1}+{t}\right)\left[\left(\mathrm{1}+{t}\right)^{\mathrm{2}} +\mathrm{1}\right]} \\…

Find-the-equation-of-the-plane-passing-through-the-points-1-0-0-and-0-1-0-and-makes-an-angle-of-pi-4-with-the-plane-x-y-3-

Question Number 55475 by Knight last updated on 25/Feb/19 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{equation}\:\mathrm{of}\:\mathrm{the}\:\mathrm{plane} \\ $$$$\mathrm{passing}\:\mathrm{through}\:\mathrm{the}\:\mathrm{points} \\ $$$$\left(\mathrm{1},\mathrm{0},\mathrm{0}\right)\:\mathrm{and}\:\left(\mathrm{0},\mathrm{1},\mathrm{0}\right)\:\mathrm{and}\:\mathrm{makes} \\ $$$$\mathrm{an}\:\mathrm{angle}\:\mathrm{of}\:\:\frac{\pi}{\mathrm{4}}\:\mathrm{with}\:\mathrm{the}\:\mathrm{plane} \\ $$$$\mathrm{x}+\mathrm{y}\:=\:\mathrm{3} \\ $$ Answered by tanmay.chaudhury50@gmail.com last updated…