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Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2281099

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4²+x² = 5²+3² x = √(5²+3²-4²) x = √(18) x = 3√(2) cm.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2281087

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18² = 14²+16²-2*14*16cosa 448cosa = 14²+16²-18² a = acos((14²+16²-18²)/448) a = 73.39845040098° (18/sin73.39845040098) = (14/sinb) b = 48.18968510422° c = 180-48.18968510422-73.39845040098 c = 58.4118644948° cotd = cota+cotb+cotc cotd = 1.80748828181  d = acot(1.80748828181) d = 28.95373454979° e = 58.4118644948-d e = 29.45812994501° f = 180-28.95373454979-73.39845040098 f = 77.64781504923° (14/sin77.64781504923) = (g/sin73.39845040098)  g = 13.73434221224 units. It implies; Area Blue...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2279591

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Let AB be 5 units. Radius, r of the inscribed circle is; 5*(2/5) r = 2 units. a = ⅛(180*6) a = 135° 2b² = 25 b = ½(5√(2)) units. c = 180-0.5(135)-45 c = 67.5° sin22.5 = ½(5√(2))/d d = 9.23879532511 units. Where d is the side length of the regular triangle (purple area). Area purple is; 0.5*9.23879532511*9.23879532511sin60 = 36.95994598698 square units. Calculating Area Shaded. e = 360-135-45-67.5-60 e = 52.5° f² = 50-50cos135 f = 9.23879532511 units. g = 52.5+0.5(45) g = 75° sin(22...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2279486

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Let alpha be x. Therefore; (12/sin2x)=(8/sinx) And; Sin2x = 2sinxcosx Therefore; (12/2sinxcos)=(8/sinx) 6 = 8cosx x = acos(6/8)° 2x = 2acos(6/8)° Let y be the third interior angle. y = (180-3acos(6/8))° It implies; Area of the triangle in cm² is; Area triangle with height 12 cm and base 8sin(180-3acos(6/8)) cm. = ½*12*8sin(180-3acos(6/8)) = 48sin(180-3acos(6/8)) cm² = 39.686269666 cm² = 39.69 cm² to 2 decimal places.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2278836

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Let the side length of the regular hexagon be 1 unit. a = ⅙(180(6-2)) a = ⅙(180*4) a = 120° a is the single interior angle of the regular hexagon. b² = 1+1-2cos120 b = 2-2cos120 b = √(3) units. b is the height of the regular hexagon. sin75 = √(3)/c c = 1.7931509443 units. c is the green length. d = ½(1.7931509443) d = 0.8965754722 units. d is half c. e = 90-75 e = 15° sin15 = f/1.7931509443 f = 0.4641016151 units. g = 1-f g = 1-0.4641016151 g = 0.5358983849 units. h² = 1+0.5358983849²-...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2277845

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Let the side length of the green regular hexagon be 1 unit. Therefore the angle theta to 2 d. p. is; (atan(0.5÷(tan72-sin60)) + atan(0.5÷(tan72+sin60)))° = (12.7389799507+7.22564879327)° = 19.964628744° ≈ 19.96°

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2276946

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2a+c = 180 c = 180-2a --- (1). 2b+d = 180 d = 180-2b --- (2). e = 180-112 e = 68° x+a+b = 180 a+b = 180-x --- (3). It implies; c+d+68 = 180 180-2a+180-2b+68 = 180 248-2(a+b) = 0 --- (4). Therefore, Calculating x. Substituting (3) in (4). 248-2(180-x) = 0 248-360+2x = 0 2x = 360-248 2x = 112 x = 56°

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2276031

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Area green exactly in cm² is; Area ABCD - Area trapezoid with parallel sides (9-2√(3)) cm and (24√(3)-39) cm, and height 6 cm. = (54-6√(3)) - ½*6((9-2√(3))+(24√(3)-39)) = (54-6√(3)) - 3(22√(3)-30) = 54-6√(3)-66√(3)+90 = 144-72√(3) = 72(2-√(3)) cm²

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2275642

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Area green is; Area triangle with height 8 unit and base 8√(3) unit - Area sector with radius 8 unit and angle 30° + Area sector with radius 8 unit and angle 60° - 2(area triangle with height 8 unit and base 8sin60 unit). = ½(8*8√(3)) - (30π*64/360) + (60π*64/360) - 2(½*8*8sin60) = 32√(3)-⅓(16π)+⅓(32π)-32√(3) = ⅓(16π) square unit.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2275162

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Let r be the radius of the circle. Calculating r. 12² = r²+a² a² = 144-r² a = √(144-r²). tanb = r/a tanb = r/√(144-r²) --- (1). tanb = a/3r tanb = √(144-r²)/(3r) --- (2). Equating (1) and (2).  r/√(144-r²) = √(144-r²)/(3r) Cross Multiply. 3r² = 144-r² 4r² = 144 r² = 36 r = 6 units. It implies, area circle is; πr² = π(6)² = 36π square units.
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