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Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2359383

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Let a be the side of the inscribed square. Calculating a. tan60 = a/b b = a/(tan60) cm. Where b is BS = CR. Therefore; 2b+a = 10 2a/(tan60)+a = 10 a((2/tan60)+1) = 10 a = 10(2√(3)-3) cm. a = 4.64101615138 cm. c = ½(10-a) c = 0.5(10-4.64101615138) c = 2.67949192431 cm. Where c = b. d = c+a d = 2.67949192431+4.64101615138 d = 7.32050807569 cm. Where d is BR. e = atan(4.64101615138/7.32050807569) e = 32.37365912705° It implies; Calculating TI, let it be f. tan32.37365912705 = f/g g = f/...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2289190

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Let the side length of the regular Pentagon be 1 unit. Therefore Area Pentagon is; (5*1)÷(4tan(180/5)) = 5/(4tan36) space unit. = 1.72047740059 space unit. Area star is; 5(area triangle with height 0.61803398875 unit and base 0.61803398875sin36 unit) + Area regular Pentagon with side 0.38196601125 unit. = 5(0.5*0.61803398875*0.61803398875sin36) + ((5*0.38196601125²)/(4tan(180/5))) = 0.56128497072 + 0.25101426986 = 0.81229924058 space unit. It implies; Area Star ÷ Area Pentagon to 3 d. p....

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/2272792

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Side length of the square is; Let it be x. x = √((16*34)-144) x = √(400) x = 20 cm. Therefore; Area Orange exactly in decimal cm² is; Half area square with side 20 cm - Area triangle with height 7.88405797101 cm and base ⅓(32sin(2atan(3/5))) cm - Area triangle with height 8.74642784227 cm and base (12sin(atan(5/3))) cm = ½(20²) - ½(7.88405797101*⅓(32sin(2atan(3/5)))) - ½(8.74642784227*(12sin(atan(5/3)))) = 200 - 37.1014492753 - 45 = 155 - 37.1014492753 = 117.898550725 cm² = 117.8 cm² to 1...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2255632

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cos30 = r/(1-r) Where r is the radius of each of the three congruent inscribed circles. It implies; 2r = √(3) - √(3)r r = √(3)/(2+√(3)) r = (2√(3)-3)/(1) r = (2√(3)-3) unit. r = 0.46410161514 unit.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2246027

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The side of area green, inscribed square is; Let it be x. Therefore; 1.11496246101x + 0.82101781219x = 27.3672604063 1.9359802732x = 27.3672604063 x = 14.1361256544 cm Therefore; Exact perimeter of green area in decimal cm is; 4(14.1361256544) = 56.5445026176 cm

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2244589

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Let AC be 1 unit. Area smaller pentagon is; ½(5)*(1/(2tan(36))) = 1.72047740059 square units. a² = 1²+0.5²-cos108 a = 1.24860602048 units. Where a is CD. (1.24860602048/sin108) = (0.5/sinb) b = 22.38617755917° c = 108-22.38617755917 c = 85.61382244083° Calculating Area E. It is; 0.5*0.5*0.5*1.24860602048sin22.38617755917 = 0.05944103227 square units. (a) Area E ÷ Area Smaller Pentagon to 3 decimal places is; 0.05944103227 ÷ 1.72047740059 = 0.03454915028  ≈ 0.035 Calculating r, radius...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2180105

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Let the square side be 2 units. Area Square is; 2² = 4 square units. tana = 2/1 a = atan(2) b = 180-2a b = (180-2atan(2))° (1/sin(180-2atan(2))) = (c/sin(atan(2))) c = 1.1180339887 units. d² = 1.1180339887²+1²-2*1.1180339887cos(90+atan(2)) d = 2.0615528128 units. e² = 2²+1² e = √(5) e = 2.2360679775 units. f = 2.2360679775+1.1180339887 f = 3.3541019662 units. g² = 3.3541019662²+2²-2*2*3.3541019662cos(atan(0.5)) g = 1.8027756377 units. (1.8027756377/sin(atan(0.5))) = (3.3541019662/sinh...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2179361

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Let the red square side be 1 unit. Area Red is; 1² = 1 square units. Calculating Area Blue. (1/sin30) = (a/sin126) a = 1.6180339887 units. a = 2sin126 units. It implies; Area Blue is; 0.5*2sin126sin24 = sin24sin126 square units. Therefore; Area Blue ÷ Area Red exactly is; sin24sin126÷1 = sin24sin126 = 0.3290568565 exactly in decimal. Calculate Alpha to 1 decimal place. b = 180-100  b = 80° c = 126-80 c = 46° (1/sin30) = (d/sin24) d = 0.8134732862 units. (0.8134732862/sin30) = (e/si...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2116605

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Let the regular triangle side length be 2 units. Therefore the square side length is 1 unit. a² = 2(1²) a = √(2) units. b² = 2+1-2√(2)cos105 b = √(3-2√(2)cos105) units. (√(3-2√(2)cos105)/sin105) = (√(2)/sinc) c = 45° (1/sin75) = (d/sin45) d = 0.7320508076 units. d = (√(3)-1) units. Area Blue is; 0.5*1*0.7320508076sin60 = 0.3169872981 square units. = ¼(3-√(3)) square units. Calculating Area Red. sin30 = e/1 e = ½ units. (2/sin75) = (f/sin45) f = 1.4641016151 units. f = (2√(3)-2) units...
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