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Mathematics Question and Solution.

https://onlineedumath.com/update/mathematics-question-and-solution/2095204

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Le the side of the regular hexagon be 1 unit. cosa = 0.5/1 a = 60° b = 60-36 b = 24° c = 108-24 c = 84° Therefore; The required angle, x is; ½(180-84) = ½(96) = 48°

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2094967

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Sir Mike Ambrose is the author of the question. Let the side of the square be 1 unit. Area square is; 1² = 1 square unit. 1 = ½+¼-½(√(2))cosa ½(√(2))cosa = ¾-1 a = acos(-√(2)/4) a = 110.70481105464° b = 180-a b = 69.29518894536° c = 90-b c = 20.70481105464° (1/sin110.70481105464) = (1/2sind) d = asin(sin110.70481105464/2) d = 27.88556683609° Area S is; Area Semicircle with radius ½ unit - Area triangle with height ½ unit and base ½(sin(2*69.29518894536) units - 2(area sector with radi...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2094966

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Sir Mike Ambrose is the author of the question. Let the length of the rectangle be 2 units. Length AB is: √(2) units. a² = 2+1-2√(2)cos75 a = √(4-√(3)) units. (a) Let Alpha be x. Calculating x. (1/sinx) = (√(4-√(3))/sin75) x = asin(sin75/√(4-√(3))) x = 39.89609063893° Area yellow is; Area triangle with height (2√(2)-√(6)) units and base 0.40352376128sin39.89609063893 units = 0.5*(2√(2)-√(6))*0.40352376128sin39.89609063893 = 0.04903810568 square units. Area Red i...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2093535

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Let the side length of the regular decagon be 1 unit. a = (180*8)/10 a = 144° a is a interior angle of the regular decagon. b = 144-120 b = 24° c² = 2-2cos24 c = 0.41582338164 units. d = ½(180-24) d = 78° e = 360-120-90-78 e = 72° f = 144-78 f = 66° g = 180-66-72 g = 42° (0.41582338164/sin42) = (h/sin72) h = 0.59102293779 units. Area Orange is; 0.5*1*1sin24+0.5*0.59102293779*0.41582338164sin66 = 0.20336832154+0.11225699415 = 0.31562531569 square units. Calculating Purple Area. j =...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2092520

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tan30 = 6/a a = 6√(3) cm. a = 10.39230484541 cm. sin30 = 6/b b = 12 cm. cos15 = c/12 c = (3√(6)+3√(2)) cm. c = 11.59110991547 cm. d = 11.59110991547²+10.39230484541²-2*11.59110991547*10.39230484541cos45 d = 8.48528137424 cm. (8.48528137424sin45) = (11.59110991547/sine) e = 75° f = √(100) f = 10 cm. g = 75-atan(3/4) g = 38.13010235416° cos38.13010235416 = h/10 h = 7.86610731855 cm. j² = 7.86610731855²+8²-2*7.86610731855*8cos75 j = 9.65925826289 cm. (9.65925826289/sin75) = (7.8661073185...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2092454

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11-2 = (x²/4) x = √(36) x = 6. Calculating Ax, let it be a. (Area Under the curve at x = a and x = 6)(1/(6-a)) = (19/3) (30-(a³/12)-2a) = (114-19a)/3 360-a³-24a = 456-76a a³-52a+96 = 0 a = 2. Calculating Ay. Notice; Ax = 2 Ay = ¼(2²)+2 Ay = 3 Therefore; Shaded Area exactly is; Area Rectangle with length 11 units and width 4 units - (Area under the curve at x = 2 and x = 6) (11*4)-(76/3) = 44-(76/3) = ⅓(132-76) = ⅓(56) square units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2088640

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Let the green and purple color regular triangle side be a. b = √(4²+2²) b = 2√(5) units. c = 0.5b c = √(5) units. d = √(8²+4²) d = 4√(5) units. e = √(a²+(a/2)²) e = √(5a²/4) e = ½(√(5)a) Calculating a, side length of the green and purple regular triangle. d-c = e 4√(5)-√(5) = ½(√(5)a) 3√(5) = ½(√(5)a) 3 = ½(a) a = 6 units. sin60 = f/3 f = ½(3√(3)) units. cos60 = g/3 g = (3/2) units. h = 6-(3/2) h = (9/2) units. j = 12+(9/2) j = (33/2) units. tank = (3√(3)/2)/(33/2) k = atan(√(3)/11)...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2087015

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Notice; The regular hexagon side length is 4 units. a² = 8-8cos120 a = √(12) a = 2√(3) units. sin60 = b/2 b = √(3) units. c = a+b c = 3√(3) units. sin30 = d/2 d = 1 unit. e = 4+4+1 e = 9 units. tanf = 3√(3)/9 f = atan(√(3)/3)° f = 30° sin30 = 3√(3)/g g = 6√(3) units. h² = 32-32cos120 h = √(48) h = 4√(3) units. tanj = 4√(3)/2 j = atan(2√(3))° k = 180-30-atan(2√(3))-60 k = (90-atan(2√(3))° l = 180-60-(90-atan(2√(3)) l = (30+atan(2√(3)))° m = (30+atan(2√(3)))-90 m = (atan(2√(3))-60)°...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2086941

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Sir Mike Ambrose is the author of the question. Let the square side be a. calculating a. b = (45-atan½) c = ½(√(2)a) units. d = ½(√(2)a)sin(45-atan½) c = ½(√(2)a)cos(45-atan½) It implies; ½*½(√(2)a)cos(45-atan½)*½(√(2)a)sin(45-atan½)+7 = ½*a*½(a) (3a²/40) + 7 = ¼(a²) 3a²+280 = 10a² 7a² = 280 a = √(40) a = 2√(10) units. Area Lilac exactly in square units is; Area triangle with height 3.4205262753 units and base ½(5√(2))sin(atan(4/7)) = 0.5*3.4205262753*½(5√(2))sin(atan(4/7)) = 3 square units....

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2086935

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Sir Mike Ambrose is the author of the question. Let AC = 1 unit. Area Yellow is; Area triangle with height ⅕(4√(5)) units and base ⅕(2√(5)) units - Area triangle with height 1 unit and base ½ unit. = ½*⅕(4√(5))*⅕(2√(5)) - ½*½*1 = ⅘-¼ = (11/20) square units. Area Red is; Area triangle with height (6/5) units and base ⅗ units. = ½*⅗*(6/5) = (9/25) square units. Area Red ÷ Area Yellow exactly is; (9/25) ÷ (11/20) = 36/55
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