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Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/1985254

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Let AB be 1 unit. (1/sin150) = (a/sin20) a = 0.68404028665 units. a is AD. Notice; AB = AC = 1 unit. (CD)² = 1+0.68404028665²-2*0.68404028665cos30 CD = 0.53208888624 units. Therefore, the required angle x is; (0.68404028665/sinx) = (0.53208888624/sin30) x = 40°

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/1985182

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Let the radius of the green circle be r. sina = (3+2√(3))/(6+4√(3)) a = asin(½) a = 30° It implies; cos30 = (3+2√(3))/((3+2√(3))+r) 6+4√(3) = 3√(3)+6+√(3)r √(3) = √(3)r r = 1 unit.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/1984724

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(3/sin108) = (EG/sin18) EG = 0.9747590887 units. (3/sin108) = (EF/sin54) EF = 2.55195242506 units. AF = 4-2.55195242506 AF = 1.44804757494 units. sin18 = a/1.44804757494  a = 0.44747130932 units.  cos18 = b/1.44804757494 b = 1.37717508205 units. b is the height of the trapezoid. Let BJ be x. c = (2-x) units. d² = 1.44804757494²+2²-4*1.44804757494cos108 d = 2.80833171413 units. (2.80833171413/sin108) = (2/sine) e = 42.63384501172° f = 72-42.63384501172   f = 29.36615498828° g² = 3²+2...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/1983938

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Let the height and base of the rectangle be x and y respectively. Let the inscribed circle's radius be r. Therefore; 0.5xy = 36 xy = 72 square units. Therefore; y = 72/x --- (1). x = 2r --- (2). Substituting (2) in (1). y = 72/2r y = 36/r units. Let theta be a. tana = x/y tana = 2r/(36/r) tana = (r²/18) --- (3). Calculating r. cos30 = 3/r r = 3/(½√(3)) r = 6/√(3) r = 2√(3) --- (4). Substituting (4) in (3). tan(r²/18), and r is 2√(3) units. tan...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/1982892

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Let the radius of the large circle be 1 unit. Diameter of the large circle = 2 units. sin60 = 2/a a = ⅓(4√(3)) units. Where a is the side length of triangle ABC. b² = 2-2cos b = √(3) units. c = a-b c = ⅓(√(3)) units. (d/sin50) = (4√(3)/(3sin100)) d = 1.79639514045 units. e² = (⅓(2√(3)))²+1² e = ⅓√(21) units. 1² = (⅓√(21))²+f²-2*⅓√(21)f cos(atan(3/(2√(3))-10) f² - 2.62161244054f + 1.33333333333 = 0  f = 1.93113 units. g² = 1.93119²+(⅓(4√(3)))²-2*1.93119(⅓(4√(3)))cos10 g = 0.5277832777...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/1980682

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Let the regular pentagon side be 1 unit. sin54 = a/1 a = 0.80901699437 unit. b = 2a b = 1.61803398875 units. Let the regular hexagon side be c. Calculating c. c+2(csin30) = b c+2(0.5c) = 1.61803398875 c = 0.80901699437 unit. Calculating Area Yellow. It is; Area regular pentagon with side 1 unit - Half Area regular hexagon with side 0.80901699437 unit - Area triangle with height 1 unit and base sin108 units. = ½(5*1)*(1/(2tan(180/5))) - ½*½(0.80901699437²*6)*(1/(2tan(180/6))) - ½*1*sin...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/1978951

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Radius of the semi circle is 12 cm. Angle AED = atan(½)° sin(atan½) = a/24 a = 10.733126292 cm. a = AF. cos(atan½) = b/12 b = 21.466252584 cm. b = EF. cos(atan2) = c/10.733126292 c = 4.8 cm. d = 12-4.8 d = 7.2 cm. e² = 7.2²+6² e = 9.37229961109 cm. f = atan(6/7.2) f = 39.80557109227° (12/sin39.80557109227) = (7.2/sing) g = 22.58853878798° h = 180-22.58853878798-39.80557109227 h = 117.60589011975° (i/sin117.60589011975) = (12/sin39.80557109227) i = 16.61063807106 cm. j = 16.610638071...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/1978112

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a² = 2*12²-2*12²cos120 a = 12√(3) cm. a = 20.78460969083 cm. a = AB. b = 2a b = 24√(3) cm. b = 41.56921938165 cm. b = AC. c² = 12²+41.56921938165²-24*41.56921938165cos30 c = 31.74901573277 cm. c = CO1 (31.74901573277/sin30) = (12/sind) d = 10.89339464913° d = Angle O1CA. e = 180-10.89339464913-30 e = 139.10660535087° e = Angle AO1C. f = asin(12/31.74901573277)  f = 22.2076542986° f = Angle O1CD. cos22.2076542986 = g/31.74901573277 g = 29.39387691339 cm. g = CD. h = 2*10.89339464913 h =...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/1978111

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Let the regular octagon side be 2 units.   Area Octagon is; ½(8*2)*(2/(2tan(180/8))) = 8/(tan(180/8)) = 19.31370849898 square units. Calculating Area Red. a = ⅛(180*6) a = 135° Let the square side be b. Calculating b. (b/tan60)+(b/tan45)+b = 2 b = 2/(1+(1/tan60)+(1/tan45)) b = 0.77599076226 unit. Area Red is; b² = 0.77599076226² = 0.60216166311 square units. Therefore; Area Octagon ÷ Area Red to 2 decimal places is; 19.31370849898 ÷ 0.60216166311 = 32.07395900816   ≈ 32.07

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/1977555

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OD = DM = 6√(2) cm. a = atan(6√(2)/12)  a = 35.26438968275° a = Angle OCD = Angle CDM.  tan35.26438968275 = b/(6√(2)) b = 6 cm. b = EM. EN = 6√(2)-6 cm. EN = 2.48528137424 cm. c = 12+6√(2)-6 c = 6+6√(2) cm. d = atan(6√(2)/(6+6√(2))) d = 30.36119340482° d = Angle EAD. sin30.36119340482 = 6√(2)/e e = 16.78759591159 cm. cos30.36119340482 = 12/f f = 13.90729981244 cm. Therefore; Length EF is; 16.78759591159-13.90729981244  = 2.88029609915 cm.
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