Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2312970

Area of coloured region is; Area triangle with height 53.3479501083 m and base 60sin(102.042575143) m + Area triangle with height 100.027406452 m and base √(5924)sin(12.5245961777) m = (½*53.3479501083*60sin(102.042575143)) + (½*100.027406452*√(5924)sin(12.5245961777)) = 1565.21739131 + 834.782608691 = 2400 m²

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2301614

Sir Mike Ambrose is the author of the question. AB exactly is; = 16tan(3acos(8/9)) - 2√(17) = 2(8tan(3acos(8/9))-√(17)) cm = 102.760478669 cm

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2255511

Area blue is; Area square with side 10 cm - Area triangle with height 5 cm and base 10 cm - Area triangle with height 10 cm and base (4.71404520791sin45) cm - Area triangle with height 5 cm and base (4.71404520791sin45) cm - Area triangle with height 5 cm and base (2.2360679775sin(atan(2))) cm = 10² - ½(10*5) -½(10*4.71404520791sin45) - ½(5*4.71404520791sin45) - ½(5*2.2360679775sin(atan(2))) = 100 - 25 - ⅓(50) - ⅓(25) - 5 = 70 - ⅓(50) - ⅓(25) = ⅓(210-75) = ⅓(135) cm² = 45 cm²

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2241064

tana = 12/8 a = atan(3/2)° b = 180-a b = (180-atan(3/2))° (10/sin(180-atan(3/2))) = (4/sinc) c = 19.4400348282° d = 180-b-c d = 180-19.4400348282-(180-atan(3/2)) d = 36.8698976458° e = 90-d e = 90-36.8698976458 e = 53.1301023542° It implies, Area S (shaded area green) is; Area trapezoid with height 12 units, and parallel sides 4 units and 12 units respectively - Area triangle with height 10 units and base 4sin36.8698976458 units - Area sector with radius 10 units and angle 53.1301023542°...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2229363

Let AB be 2 unit. Therefore CD = 1 unit. It implies; Area Blue is; Area triangle with height 0.72111025509 unit and base sin(atan(3/2)) unit. = 0.5*0.72111025509sin(atan(3/2)) = 3/10 space unit. Area Green is; Area trapezoid with two parallel side (3/2) unit and 1 unit, and height ½ unit - Area triangle with height (3/2) unit and base ½ unit. = ½*½((3/2)+1) - ½*½(3/2) = (5/8) - (3/8) = ¼ space unit. Area Red is; Area triangle with height tan(atan(2/3)) unit and base √(2)sin45 unit - Area...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2217048

Let the side length of the regular heptagon be 1 unit. a = ⅐(180(7-2)) a = 128.5714285714° Where a is the single interior angle of the regular heptagon. b² = 2-2cos128.5714285714 b = 1.8019377358 units. c = ½(180-128.5714285714) c = 25.7142857143° d = 128.5714285714-25.7142857143 d = 102.8571428571° e² = 1.8019377358²+1-2*1.8019377358cos102.8571428571 e = 2.2469796037 units. Where e is r+q+p. (2.2469796037/sin102.8571428571) = (1/sinf) f = 25.7142857144° g = 180-25.7142857144-102.85714...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2203282

Sir Mike Ambrose is the author of the question. Let the two equal lengths be 1 unit. (a) Calculating Theta exactly. Let theta be x. Calculating x. x = ½(90-54) x = ½(36) x = 18° sin18 = a/1 a = 0.30901699437 unit. b = 90-18 b = 72° sin72 = c/1 c = 0.9510565163 unit. tan36 = 0.9510565163/d d = 1.30901699437 units. Area Blue is; 0.5(1.30901699437*0.9510565163) = 0.62247457122 square units. e = 270-54-96 e = 120° f = 360-120-72 f = 168° g² = 2-2cos168 g = 1.98904379074 units. h = ½(180-...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2191257

Let the side of the inscribed square be 2 unit. Therefore; Area S is; Area triangle with two side 1.03528 unit and 0.53589838486 unit, and angle 45° = 0.5*1.03528*0.53589838486sin45 = 0.1961531464 space unit. Area R is; Area triangle with two side (2√(2)-2) unit and 0.65961372961 unit, and angle 72.367664609° = 0.5*(2√(2)-2)*0.65961372961sin72.367664609 = 0.26038499708 space unit. Area T is; Area sector with radius 2√(2) unit and angle 30° - Area triangle with two side 2√(2) unit and 2 u...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2187818

tana = 8/13 a = atan(8/13)° tan(atan(8/13)) = b/10 b = 80/13 units. It implies; Area Blue1 is; ½*10(80/13) = (400/13) square units. = 30.7692307692 square units. Calculating Area Blue2. c² = 10²+8² c = √(164) c = 2√(41) units. d² = 8²+13² d = √(233) units. 233 = 9+164-12√(41)cose 12√(41)cose = 173-233 e = acos((173-233)/(12√(41))) e = acos(-5/√(41))° e = 141.3401917459° f = e-90 f = (acos(-5/√(41))-90)° tan(acos(-5/√(41))-90) = g/3 g = 3.75 units. g = ¼(15) units. h = 12-g h = 12-¼(1...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2162533

Sir Mike Ambrose is the author of the question. Notice; Side length of the congruent regular hexagon is 2 units. (a) Calculating Length Blue ÷ Length Red. Length Blue is; Let it be x. 4²=2²+x²-4xcos150 x²+2√(3)x-12= 0 It implies; x (Length Blue) = (√(15)-√(3)) units. Length Red is; Let it be y. y = √(8-8cos120)-x y = 2√(3)-(√(15)-√(3)) It implies; y (Length Red) = (3√(3)-√(15)) units. Therefore; Length Blue ÷ Length Red exactly is; (√(15)-√(3)) ÷ (3√(3)-√(15)) = ½(√(5...

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