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Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3703419

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Calculating angle x.Let the two congruent lengths be 1 unit each.a = 180-21-102a = 57°b = 180-102-36b = 42°c = 180-a-bc = 180-57-42c = 81°(1/sin42) = (d/sin102)d = 1.4618186516 units.(1/sin21) = (e/sin102)e = 2.72945056045 units.It implies;f² = d²+e²-2decos81f² = 1.4618186516²+2.72945056045²-2*1.4618186516*2.72945056045cos81f = 2.8876424765 units.It implies, the required angle x is;(2.8876424765/sin81) = (2.72945056045/sinx)sinx = 0.9335804265x = asin(0.9335804265)x = 69°

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3702062

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Calculating y to 1 decimal place.It implies;a = 3125 m.a is the base of the composite plane shape.b = (3125+y) m.c = 90-60c = 30°It implies;Length y to 1 decimal place is;tan30 = a/b1/√(3) = 3125/(3125+y)3125+y = 3125√(3)y = 3125√(3)-3125y = 3125(√(3)-1) m Exactly.y = 2287.65877365 m.y = 2287.7 m to 1 decimal place.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3701659

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Calculating 74L.Notice.L is the side length of the inscribed yellow square.tana = 3/4a = atan(3/4)°b = 90-ab = atan(4/3)°it implies;tana = L/xtan(atan(3/4)) = L/x3/4 = L/xx = ⅓(4L) cm.tanb = L/ytan(atan(4/3)) = L/y4/3 = L/yy = ¼(3L) cm.It implies, length L is;x+L+y = 5⅓(4L)+L+¼(3L) = 516L+12L+9L = 6037L = 60L = 60/37 cm.Again, L is the side length of the inscribed yellow square.Therefore, 74L is;74*(60/37)= 2*60= 120 cm.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3701655

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Calculating R, the radius of the blue circle.a = ½(4)a = 2 units.b = 9-ab = 9-2b = 7 units.c²+2² = R²c = √(R²-4) units.d = 7-cd = (7-√(R²-4)) units.It implies R, radius of the blue circle is;R² = b²+d²R² = 7²+(7-√(R²-4))²R² = 49+49-14√(R²-4)+R²-40 = 98-14√(R²-4)-414√(R²-4) = 947√(R²-4) = 4749(R²-4) = 220949R²-196 = 220949R² = 2405R² = 2405/49R = √(2405/49)R = ⅐√(2405) units.R = 7.00582847728 units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3699325

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Calculating Blue Area.Let 2x units be the radius of the ascribed quarter circle.½(2x) = x units.x is the radius of the inscribed yellow (20 square units) and white half circle.Calculating x.a = ½(90)a = 45°b² = 2x²b = √(2)x units.b is the radius of the inscribed yellow (20 square units) and white quarter circle.It implies;Area quarter circle with radius x units + Area sector with radius √(2)x units and angle 45° - Area isosceles right-angled triangle with equal side lengths x units = 20(¼(x²)π)...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3699322

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Calculating R, radius of the inscribed yellow circle.a = ¼(180)a = 45°b = 180-ab = 135°c = ½(a)c = 22.5°d = b-cd = 135-22.5ald = 112.5°e = 180-a-de = 180-45-112.5e = 22.5°tan22.5 = 2/ff = 4.82842712475 units.g² = f²+2²g = √(4.82842712475²+2²)g = 5.22625185951 units.g is the diameter of the inscribed half circle.h = ½(g)h = 2.61312592975 units.h is the radius of the inscribed half circle.tan(0.5*22.5) = R/jj = 5.02733949213R units.k = j-hk = (5.02733949213R-2.61312592975) units.l = h-Rl = (2.613...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3698086

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Calculating angle x.Notice.The composite plane shape is not drawn to scale.Let the three equal lengths be 1 unit each.It implies;AB = BD = DE = 1 unit.Let y be CD.a = (1+y) units.a is BC.Calculating y.tan15 = 1/atan15 = 1/(1+y)tan15+ytan15 = 1y = (1-tan15)/(tan15)y = 2.73205080757 units.Again, y is CD.(2.73205080757/sinb) = (1/sin15)sinb = 2.73205080757sin15b = asin(0.70710678119)b = 45°b is the supplementary angle of angle CED.c = 180-bc = 180-45c = 135°c is angle CED.It implies, the required...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3696224

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Calculating Angle Theta.Let theta be a, angle CAD.b = 180-40-80b = 60°b is angle BCD.Let X = 1 unit.X is BD.(1/sin60) = (Y/sin80)Y = 1.1371580426 units.Y is BC.(c/sin40) = (1/sin60)c = 0.74222719897 units.c is CD.It implies;X+Y = 1+1.1371580426X+Y = 2.1371580426 units.X+Y is AC.d = 180-80d = 100°d is angle ADC.Therefore;Calculating theta, a (angle CAD).((X+Y)/sind) = (c/sina)(2.1371580426/sin100) = (0.74222719897/sina)sina = (0.74222719897sin100)/(2.1371580426)a = asin((0.74222719897)/(2.137158...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3696222

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Calculating the required red angle.Let it be x.Notice.The composite plane shape is not drawn to scale.Let the both equal lengths that makes the hypotenuse of the ascribed right-angled triangle be 1 unit each.Let the other two equal lengths of the ascribed right-angled triangle be y each.a = 1+1a = 2 units.It implies;y ~ b2 ~ 1Cross Multiply.b = ½(y) units.c = 90-75c = 15°Calculating y.sin15 = b/1sin15 = 0.5yy = sin15/0.5y = ½(√(6)-√(2)) units.y = 0.51763809021 units.d² = 1²+0.51763809021²-2*1*0...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3695505

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Calculating length BA, diameter of the small half circle.a = 3+12+5a = 20 units.a is the diameter of the big half circle.b = ½(a)b = ½(20)b = 10 units.b is the radius of the big half circle.Let x be the radius of the small half circle.c²+x² = 10²c² = 100-x²c = √(100-x²) units.d = ½(12)d = 6 units.x² = 6²+e²e² = x²-36e = √(x²-36) units.f = 10-3-6f = 1 unit.It implies, x is;e²+f² = c²√(x²-36)²+1² = √(100-x²)²x²-36+1 = 100-x²2x² = 100+35x² = ½(135)x = √(67.5) units.Again, x is the radius of the sm...
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