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Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3054308

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Let the radius of the semi circle be 1 unit. cos20 = a/2 a = 1.87938524157 units. cos20 = 1/b b = 1.06417777248 units. c = a-b c = 0.81520746909 unit. Where c is AB, the side of the square.  Area Square is; (0.81520746909)² = 0.66456321766 square units. Calculating AF. sin20 = d/2 d = 0.68404028665 units. 0.68404028665 = e 1.87938524157 = 0.81520746909 cross multiply. 1.87938524157e = 0.81520746909*0.68404028665 e = 0.2967112535 unit. f² = 0.2967112535...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3052669

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Let the side of the regular pentagon be 1 unit. Calculating Area Red. a² = 1²+1²-2*1*1cos108 a = 1.61803398875 units. b = 108-36-60 b = 12° (c/sin12) = (1.61803398875/sin96) c = 0.33826121272 unit. d = 1-c d = 0.66173878728 unit. e = 96-60 e = 36° tan36 = f/0.66173878728 f = 0.48078137139 unit. Area Red is; ½(df) = 0.5*0.48078137139*0.66173878728 = 0.15907584083 square units. Calculating Area Lilac. sin36 = 0.48078137139/g g = 0.81795412443 units....

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3051425

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a² = 15²+12²-2*12*15cos120 a = 23.43074902772 cm. Where a is the side length of the equilateral triangle ABC. (23.43074902772/sin120) = (12/sinb) b = 26.32950349168° c = 60-b c = 33.67049650832° d² = 15²+15²-2*15*15cos120 d = 25.98076211353 cm. e = atan(7.5/25.98076211353) e = 16.10211375199° f = 90-e f = 73.89788624801° g = 180-f-c g = 72.43161724367° (15/sin72.43161724367) = (h/sin73.89788624801) h = 15.11661227595 cm. i = a-h  i = 8.31413675177 cm. L...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3049712

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Sir Mike Ambrose is the author of the question. Let the side length of triangle ABC be 1 unit. a = 120-78 a = 42° b = 60-42 b = 18° (1/sin42) = (c/sin18) c = 0.4618186516 unit. tan60 = d/0.5 d = 0.86602540378 unit. Area Green is; 0.5*0.4618186516*0.86602540378 = 0.19997334211 square units. e = ⅓ unit. Where e is the side length of the red inscribed regular hexagon. Area Red is; ½*6*(⅓)²*(1/2tan(30)) = ⅓*(1/2tan(30)) = 0.28867513459 square units. f...

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

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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...
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