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Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2527944

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Calculating angle x. Notice! The inscribed triangle is isosceles. Let the base be 1 unit. It implies; a = 180-80-40 a = 60° (b/sin80) = (1/sin60) b = 1.1371580426 units. (1/sin20) = (c/sin80) c = 2.8793852416 units. d = ½(c) d = 1.4396926208 units. cos10 = 1.4396926208/e Where r is the radius of the circle. e = 1.4396926208/cos10 e = 1.4619022001 units. Again, e is the radius of the circle. f² = 1.4619022001²+1.1371580426²-2*1.1371580426*1.4619022001cos30...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2526890

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Blue area is; Area sector with radius 3√(2) unit and angle 30° - area isosceles triangle with two equal length 3√(2) unit and angle 30°. = (30πx(3√(2))²÷360) - (0.5x(3√(2))²sin30) = (18π)/12 - (9/2) = (3π)/2 - (9/2) = ½(3(π-3) square unit. = 0.21238898039 square unit.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2526574

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a² = 5²+2.5²-2*5*2.5cos120 120° is the single interior angle of the regular hexagon. it implies; a = 6.6143782777 units. (6.6143782777/sin120) = (2.5/sinb) b = 19.1066053509° c = 120-b c = 100.8933946491° d² = 6.6143782777²+1-2*6.6143782777cos100.8933946491 d = 6.8738635424 units. Therefore, area inscribed right-angled triangle is; 0.5*6.8738635424*6.6143782777 = 22.7331668494 square units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2526144

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Calculating x. a²+(x-3)² = 10² a² = 100-x²+6x-9 a² = 91+6x-x² a = √(91+6x-x²) cm. It implies; (a+x)² = (x-3)²+(x+4)² (√(91+6x-x²)+x)² = x²-6x+9+x²+8x+16 91+6x-x²+2x√(91+6x-x²)+x² = 2x²+2x+25 2x√(91+6x-x²) = 2x²-4x-66 x√(91+6x-x²) = x²-2x-33 x²(91+6x-x²) = (x²-2x-33)² 91x²+6x³-x⁴ =x⁴-2x³-33x²-2x³+4x²+66x-33x²+66x+1089 91x²+6x³-x⁴ = x⁴-4x³-62x²+132x+1089 2x⁴-10x³-153x²+132x+1089 = 0 Resolving the above fourth power equation. It implies; x = 11 units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2526022

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Calculating Length MN. Let BD = a. b = 180-30-75 b = 75° b is angle BDC. Notice! Area ABCD = 10 square units. Calculating a. It implies  0.5*3*a*sin60 + 0.5*a²sin30 = 10 ¼(3√(3)a+¼(a²) = 10 ¼(3√(3)a+a²) = 10 a²+3√(3)a-40 = 0 Resolving the above quadratic equation via completing the square approach to get a. a²+3√(3)a-40 = 0 (a+½(3√(3)))² = 40+(0.5*3√(3))² (a+½(3√(3)))² = 40+¼(27) (a+½(3√(3)))² = ¼(160+27) (a+½(3√(3)))² = ¼(187) a+½(3√(3)) = √(¼(187)) a = -½...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2525806

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Notice! The composite plane shape consist of two half circles with equal diameter, 10 units each. Radius = 5 units each. Calculating shaded area. a = 180-2*30 a = 120° Shaded Area is; Area semi circle with radius 5 units - Area sector with radius 5 units and angle 120° + Area triangle with height 5 units and base 5sin120 units + Area sector with radius 10 units and angle 30° - Area triangle with height 5 units and base 5sin120 units - Area sector with radius 5 units and ang...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2523942

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Let the single side length of the equilateral triangle be 4 unit. Therefore; Shaded area ÷ Area circle exactly in decimal is; (Area sector with radius √(3) unit and angle (180-2(sin–¹(sin60÷√(13))+30)) - Area isosceles triangle with two equal length √(3) unit and the angle they form, angle (180-2(sin–¹(sin60/√(13))+30))) ÷ (Area circle of radius √(3) unit). = ((180-2(sin–¹(sin60÷√(13))+30))xπ(√(3))²÷360 - ½((√(3))²xsin(180-2(sin–¹(sin60÷√(13))+30)))) ÷ (3π) = (2.4139010313 - 1.4...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2523732

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sin15 = a/6 a = 1.5529142706 units. a is CD. cos15 = b/6 b = 5.7955549577 units. b is BD. c² = 4²+6²-2*4*6cos30 c = 3.2296719057 units. c is AC. (3.2296719057/sin30) = (4/sind) d = 38.2619661997° d is angle ACB. e = (90-15)-d e = 75-38.2619661997 e = 36.7380338003° e is angle ACD. tan36.7380338003 = f/1.5529142706 f = 1.1591109915 units. f is DE. Therefore, area triangle ADE is; Area triangle with height 3.2296719057 units and base 1.5529142706sin36.738033800...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2522593

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Shaded blue area will be; 5(area square of single side length 2 cm) - area semi circle of radius 2 cm. =5(2x2) - ½(4π) = 20-2π = 2(10-π) cm²

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2522568

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Green area will be; ½(area quarter circle with radius (2+√(2)) unit) - area isosceles right-angled triangle with height and base √(2) unit respectively - area sector with radius √(2) unit and angle 135° = ½(¼(2+√(2))²π) - (½(√(2))²) - (π(√(2))²x135÷360) = ¼(3+2√(2))π - 1 - ¾(π) = ¼(3π+2√(2)π-4-3π) = ¼(2√(2)π-4) = ½(√(2)π-2) square unit.
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