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Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2235317

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Area blue is: Area triangle with height 1 cm and base (3sin(109.471220634)) cm. = 0.5*1*3sin(109.471220634) = 1.41421356238 cm² = √(2) cm²

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2235311

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Let the radius of the inscribed white semi circle be r. Therefore; r²+(1+r)²=(2+r)² r²+1+2r+r²=4+4r+r² r²-2r-3 = 0 (r-1)² = 3+(-1)² (r-1)² = 4 r = 1±2 r ≠ -1 r = 3 unit. It implies; Area blue is; Area semi circle with radius 5 unit - Area semi circle with radius 3 unit. = ½(π*5²) - ½(π*3²) = ½(25π) - ½(9π) = ½(25π-9π) = ½(16π) = 8π square unit.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2235307

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Radius of the inscribed circle, r is; 2r² = 4 r² = 2 r = √(2) unit. Therefore; Area R in square unit to 3 d. p. is; Area sector with radius √(2) unit and angle atan(0.5√(2))° - Area triangle with height 0.8165 unit and base √(2)sin(atan(0.5√(2))) unit - Area sector with radius 2 unit and angle 25.5286945392° + Area triangle with height 2 unit and base (2sin25.5286945392) unit. = (atan(0.5√(2))π*√(2)²÷360) - (0.5*0.8165*√(2)sin(atan(0.5√(2)))) - (25.5286945392π*2²÷360) + (0.5*2*2sin25.5286...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2234887

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tan60 = a/10 a = 10√(3) cm. a is the height of the equilateral triangle. sin(atan(2)) = b/(10√(3)) b = 15.4919333848 cm. b is a side length of the square. It implies; Area Square is; b² = (15.4919333848)² = 240 cm²

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2233975

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Let the base of ABCD be 1 unit. a = 180-24-38-48 a = 180-110 a = 70° b = 38+48 b = 86° (1/sin70) = (c/sin86) c = 1.0615854889 units. d = 180-26-24-38 d = 180-88 d = 92° (1/sin92) = (e/sin38) e = 0.6160367483 units. f² = 0.6160367483²+1.0615854889²-2*1.0615854889*0.6160367483cos26 f = 0.5752270365 units. Let the required angle be g. Calculating g. (0.5752270365/sin26) = (0.6160367483/sing) g = 28.0000000029° It implies, g, the required angle is; = 28°

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2233902

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Let a be the side of the square. cos30 = b/8 b = 4√(3) cm. sin30 = c/8 c = 4 cm. a = b+12 a = (12+4√(3)) cm. Area Square is; a² = (12+4√(3))² = 358.27687752661 cm²  d² = 12²+4²-2*4*12cos30 d = 8.76707255797 cm. (8.76707255797/sin30) = (12/sine) e = 180-43.18678543201 e = 136.81321456799° f = 360-e-180 f = 43.18678543201° g² = 8²+8.76707255797²+2*8*8.76707255797cos43.18678543201 g = 6.21165708246 cm. (6.21165708246/sin43.18678543201) = (8.76707255797/sinh) h = 75° i = 120-75 i = 45°...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2232620

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Sir Mike Ambrose is the author of the question. Let the two equal side length of the ascribed isosceles triangle be 1 unit. Therefore; Area triangle ABC is; ½(1*1sin36) = ½(sin36) space unit. = 0.29389262615 space unit. Area purple is; Area triangle with height 0.37567713613 unit and base (0.15621533715sin138) unit. = 0.5*0.37567713613*0.15621533715sin138 = 0.01963447686 space unit. It implies; Area Triangle ABC ÷ Area Purple to 2 d. p. is; 0.29389262615 ÷ 0.01963447686 = 14.9681923407  ≈...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2232618

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Area green is; Area square with side 6 unit + 4(Area sector with radius 6 unit and angle 60° - Area equilateral triangle with side 6 unit) - Area square with diagonal (6√(3)-6) unit - 4(area sector with radius 6 unit and angle 30° - area triangle with height 6 unit and base (6sin30) unit). = 6² + 4((π6²)/6 - ¼(6²√(3))) - ½(6√(3)-6)² - 4((30π*36÷360)-½(36sin30)) = 36 + 4(6π-9√(3)) - ½(144-72√(3)) - 4(3π-9) = 36 + 24π - 36√(3) - 72 + 36√(3) - 12π + 36 = 24π - 12π = 12π space unit.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2232610

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6a = 4*17 a = ⅓(34) units. b = ½(4+17) b = ½(21) units. c = b-4 c = ½(21)-4 c = ½(21-8) c = ½(13) units. d = ½(a+6) d = ½(⅓(34)+6) d = ½*⅓(34+18) d = ½*⅓(52) d = ⅓(26) units. It implies, radius of the circle (r) is; r² = (⅓(26))²+(½(13))² r² = ⅑(676)+¼(169) r² = (676*4+169*9)/36 r² = 4225/36 r = √(4225/36) r = ⅙(65) units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2229367

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Let the square side be a. 2(a-14)² = 14² (a-14)² = 98 a = 14+7√(2) units. Green area length and width is; Length = 14+7√(2)-18 = 7√(2)-4 units. Width = 14+7√(2)-10 = 4+7√(2) units. = (4+7√(2))(7√(2)-4) = 98-16 = 82 square units.
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