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Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3048366

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a² = 12²+6² a = 6√(5) cm. a = AE. b = atan(1/2)° b = angle DAE. c = 180-atan(2) c = 116.56505117708° c = angle AFC. d = 180-116.56505117708-atan(1/2) d = 36.86989764584° (6/sin36.86989764584) = (e/sin116.56505117708) e = 8.94427191 cm. f = 6√(5)-8.94427191  f = 4.472135955 cm. g = 180-2atan(2) g = 53.13010235416° g = angle AEB. cos53.13010235416 = h/4.472135955 h = 2.683281573 cm. It implies; Area S1 is; 0.5*2.683281573*4.472135955sin53.13010235416...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3046648

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Le the side of the pentagram be 1 unit. tan54 = a/0.5 a = 0.68819096024 unit. cos54 = 0.5/b b = 0.85065080835 unit. c = b+a c = 1.53884176859 units. Let the side length of the ascribed regular hexagon be d. Calculating d. sin45 = e/d e =0.5√(2)d unit. It implies; e+d = c 0.5√(2)d+d = 1.53884176859  d = 0.90143263769 unit. f = 0.90143263769+2(0.90143263769sin45) f = 2.17625089948 units. g = ½(2.17625089948-1) g = 0.58812544974 unit. h² = 0.58812544974...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3045130

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Let the inscribed purple regular heptagon side be 1 unit. a = ⅐(180*5) a = ⅐(900)° b = 180-⅐(900)) b = ⅐(360)° c = 180-2(⅐(360)) c = ⅐(540)° (1/sin⅐(540)) = (d/sin⅐(360)) d = 0.8019377358 unit. e = 2(0.8019377358)+1 e = 2.60387547161 units. f = 90-½(⅐(540)) f = ⅐(360)° cos⅐(360) = g/2.60387547161 g = 1.62348980186 units. h = 2g h = 3.24697960372 units. Where h is the base of the ascribed quadrilateral. cos(180/7) = i/0.8019377358 i = 0.72252093395 unit....

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3043543

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Let the side of the regular pentagon be 1 unit. a² = 2-2cos108 a = 1.61803398875 units. sin30 = b/0.5 b = 0.25 unit. c = 2b c = 0.5 unit. Where c is the inscribed square side. Area Square is; (0.5)² = 0.25 square units. Inscribed circle radius d is; d = ½(b) d = 0.125 unit. e = 0.5-0.125 e = 0.375 unit. f = 2atan(0.125/0.375) f = 36.86989764584° tan36.86989764584 = g/0.5 g = 0.375 unit. Shaded Area is; 0.5*0.375*0.5-π*0.125*0.125 = 0.0446626...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3041813

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a = asin(1/3)° a = 19.47122063449°  a = angle ABF. Let the centre of the diameter of the half circle be O. Angle AOF = 90-19.47122063449 = 70.52877936551° (OC)² = 12²+18² OC = 6√(13) cm. Angle COE = acos(1/√(13)) = 73.89788624801°   Angle BOC = atan(2/3) = 33.69006752598° It implies; Angle EOF will be; 73.89788624801-(70.52877936551-33.69006752598) = 37.05917440848°  Therefore; Length EF is; (EF)² = 6²+6²-2*6*6cos37.05917440848  EF = 3.81353187415 cm...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3040149

mathematics-question-and-solution_1742774497D5FZMH.jpeg
Let the side of the regular pentagon be 1 unit. Notice; The regular pentagon side is equal the regular heptagon side. a = ⅐(180*5) a = ⅐(900)°, the single interior angle of the regular heptagon. b = 2a b = ⅐(450)° tan(⅐(450)) = c/0.5 c = 1.03826069829 units. cos(⅐(450)) = 0.5/d d = 1.15238243548 units. Where d is the radius of the ascribed circle. e = 180-⅐(900) e = ⅐(360)° tan18 = 0.5/f f = 1.53884176859 units. g² = 1.15238243548²-0.5² g = 1.03826069828 u...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3038534

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a = 360-140-80 a = 140° cos20 = 1/b b = 1.06417777248 units. (1.06417777248/sin30) = (c/sin70) c = 2 units. d² = 4+1.064177772482²-4*1.06417777248cos140 d = 2.89711998506 units. (2.89711998506/sin140) = (2/sine) e = 26.34291130662° f = 40-e f = 13.65708869338°  g = 20+26.34291130662 g = 46.34291130662° tan46.34291130662 = h/2 h = 2.09602104183 units. Area ABC is; 0.5*2*2.09602104183  = 2.09602104183 square units. Calculating Area Blue. i = 60-26.34...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3036853

mathematics-question-and-solution_1742601431tUZkNO.jpeg
Let the side of the regular pentagon be 1 unit. a = 360-2(108)-90 a = 54° tan72 = b/0.5 b = 1.53884176859 units. tan54 = 1.53884176859/c c = 1.11803398875 units. d = c-0.5 d = 0.61803398875 unit. (e/tan36)+(e/tan27) = d Where e is the radius of the inscribed circle. e = 0.61803398875/((1/tan36)+(1/tan27)) e = 0.18509595408 unit. f = 180-72-54 f = 54° Therefore; g = d = 0.61803398875 unit. Shaded Area Red is; Area triangle with height 0.61803398875 uni...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3035281

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Notice; The diameter of the semicircle is 8 units. Therefore radius is 4 units. tan30 = a/2 a = ⅔(√(3)) units. b = 3a b = 2√(3) units. c² = 2²+(⅔(√(3)))² c = (4/√(3)) units. d = (2/√(3))+c d = 2√(3) units. e² = 4²+4²-2*4*4cos120 e = 4√(3) units. f = atan((4/√(3))/2) f = atan(2/√(3)° g² = 4²+4²-2*4*4cos(180-2atan(2/√(3))) g = (8√(21)/7) units. h = (atan(2/√(3))-30)° Area Maroon exactly in square units is; Area triangle with height (8√(21)/7) units and...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3033668

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Let the side of the regular hexagon which is equal the side of the square be 1 unit. a = ½(180-108) a = 36° tan36 = b/0.5 b = 0.363271264 unit. Area Blue is; 0.5*0.363271264*0.5 = 0.090817816 square units. c² = 2-2cos120 c = 1.73205080757 units. d = c-1 d = 0.73205080757 unit. sin54 = e/f f = 1.2360679775e It implies; f+e = d 1.2360679775e+e = 0.73205080757 e = 0.32738307374 unit. Where e is the radius of the inscribed circle. Area Lilac (inscribed c...
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