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Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3671253

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Calculating area x.Let 3a be the height of the ascribed triangle.Therefore, considering the 6 square units inscribed triangle area.½*(3a)*b = 63ab = 12b = (4/a) units.b is the base of the 6 square units triangle area.c = y+bc = (y+(4/a)) units.Calculating y, the base of the area x, its height is ⅓(3a) units which is a.3a ~ ac ~ yIt implies;3 ~ 1(y+(4/a)) ~ yCross Multiply.3y = y+(4/a)2y = 4/ay = (2/a) units.Again, y is the base of area x with a it's height.d = b+yd = (4/a)+(2/a)d = (6/a) units....

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3671249

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Calculating Alpha.Let it be x.Let 1 unit be the side length of the inscribed square.Let r be the radius of the ascribed quarter circle.a² = 1²+1²a =√(2) units.a is OE, the diameter of the inscribed square.b = (r-1) units.Calculating r.1 ~ r(r-1) ~ 1Cross Multiply.r(r-1) = 1r²-r-1 = 0(r-½)² = 1+(-½)²(r-½)² = 1+¼(r-½)² = (5/4)r = ½±½√(5)It implies;r ≠ ½-½√(5)r = ½+½√(5)r = ½(1+√(5)) units.r = 1.61803398875 units.Again r is golden ratio, the radius of the ascribed quarter circle.Recall.b = r-1 un...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3669489

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Calculating green area EFB (area triangle).Notice.FO = CD.AO = BF = AE = 4 units.Where;AE and BF are the height and base of green triangle area EFB.It implies;Area EFB is;½*BF*AE= ½*4*4= 8 square units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3669479

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Calculating r, radius of the inscribed circle and area ABCD (isosceles trapezoid).Notice.Triangle AOD is a right-angled triangle tana = 3/2a = atan(3/2)°tanb = 2/3b = atan(2/3)°Calculating r, radius of the inscribed circle.sina = r/2sin(atan(3/2)) = r/2r = 1.66410058868 units.Orsinb = r/3sin(atan(2/3) = r/3r = 1.66410058868 units.Calculating Area isosceles trapezoid ABCD.c²+r² = 2²c² = 2²-1.66410058868²c = √(1.23076923075)c = 1.10940039244 units.d = 2cd = 2(1.10940039244)d = 2.21880078488 units...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3667245

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Calculating x.a² = 1²+1²a² = 2a = √(2) units.b = ⅛*180(8-2)b = ⅛*180*6b = 135°b is the single interior angle of a regular octagon with side length √(2) units. Half the regular octagon is derived to inscribe the ascribed half circle.c² = 2a²-2a²cos135c² = 2√(2)²-2√(2)²cos135c = 2.61312592975 units.Let r be the radius of the ascribed half circle.r²+r² = c²2r² = 2.61312592975²r = √(2.61312592975²/2)r = 1.84775906502 units.d²+d² = r²2d² = 1.84775906502²d = 1.30656296487 units.d is the radius of the...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3667238

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Calculating r, radius of the ascribed quarter circle.a = 2r units.a is the diameter of the complete circle (2 radius).a = ½(8)a = 4 units.b²+a² = r²b² = r²-4²b = √(r²-16) units.c = b-3c = (√(r²-16)-3) units.d = b-5d = (√(r²-16)-5) units.It implies;4 ~ cd ~ 4Cross Multiply.cd = 16(√(r²-16)-3)(√(r²-16)-5) = 16r²-16-8√(r²-16)+15 = 16r²-16-8√(r²-16) = 1r²-17 = 8√(r²-16)(r²-17)² = 64(r²-16)r⁴-34r²+289 = 64r²-1024r⁴-98r²+1313 = 0(r²-49)² = -1313+(-49)²(r²-49)² = -1313+2401r² = 49±√(1088)r² = 49±8√(17...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3666388

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Calculating area blue.a² = 15²+15²a² = 2(15²)a = √(2(15²))a = 15√(2) cm.cosb = 21/(15√(2))b = acos(21/(15√(2)))b = 8.13010235416°c = 45+bc = 53.13010235416°d² = 21²+15²-2*15*21cos53.13010235416d = 16.9705627485 cm.(16.9705627485/sin53.13010235416) = (21/sine)e = 81.8698976458°f = 90-ef = 8.13010235416°It implies the blue area is;½15*dsinf= 0.5*15*16.9705627485sin8.13010235416= 18 cm²

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3666381

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Calculating x, length AD.Let z be alpha.Let CD = y.a = (x+y) units.a is AC.b²+y² = 10²b = √(100-y²) units.b is BC.(x+y)²+√(100-y²) = 12²x²+2xy+y²+100-y² = 144x²+2xy = 442xy = 44-x²y = (44-x²)/(2x) --- (1).sinz = y/10 --- (2).cosz = √(100-y²)/10 --- (3).x² = 12²+10²-2*12*10cos(2z)x² = 244-240(cos²z-sin²z)x² = 244-240(1-2sin²z) --- (4).Substituting (2) in (4).x² = 244-240(1-2(y/10)²)x² = 244-240(1-(2y²/100)x² = 244-240+⅕(24y²)x² = 4+⅕(24y²)x² = ⅕(20+24y²)5x² = 20+24y² --- (5).Calculating x.Substi...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3665276

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Calculating the required angle.Let it be x.Let 1 unit be the side length of the three congruent squares.Let y be the side length of the green square.a = 1+1a = 2 units.b = ½(y) units.Calculating y.2² = (½(y))²+y²4 = ¼(y²)+y²¼(5y²) = 4y² = ⅕(16)y = √(⅕(16))y = ⅕(4√(5)) units.y = 1.788854382 units.Again, y is the side length of the green square.Recall.b = ½(y)b = 0.5(1.788854382)b = 0.894427191 units.c²+b² = 1²c² = 1-0.894427191²c = 0.4472135955 units.cosd = 0.894427191/1d = acos(0.894427191)d =...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3665264

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Calculating Area Red.Let x be the radius of the smallest inscribed white half circle.a = 2x units.a is the radius of the smaller inscribed white circle and also the radius of the red and smallest white circle.c = 3x units.c is the radius of the red and smaller white circle.Calculating x.4²+x² = (3x)²16+x² = 9x²8x² = 16x = √(2) units.Recall.a = 2xAnd x = √(2) units.a = 2√(2) units.Again, a is the radius of the smaller inscribed white circle and also the radius of the red and smallest white circl...
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