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Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2200038

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a = atan(⅓)° ⅓ = b/3 b = 1 unit. It implies; Area Red is; Area triangle with height 1 unit and base 3 units + ½(2(area quarter circle with radius 3 units - area triangle with height and base 3 units respectively))) = ½(1*3) + ½(2(¼(π*3²) - ½(3*3))) = ½(3) + ¼(9)π - ½(9) = ¼(9π) - ½(6) = ¼(9π-12) square units. = ¾(3π-4) square units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2199763

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Let the regular pentagon side length be 1 unit. a =⅕(180(5-2)) a = ⅕(180*3) a = 108° a is an angle of the regular pentagon. Calculate x. b = 108-90 b = 18° x = ½(180-18) x = ½(162) x = 81° c = 108-60 c = 48° d = 180-18-48 d = 114° (e/sin48) = (1/sin114) e = 0.8134732862 units. f = 1-e f = 1-0.8134732862 f = 0.1865267138 units. (0.8134732862/sin48) = (g/sin18) g = 0.3382612127 units. sin30 = 0.25/h h = 0.5 units. j = 0.5-g j = 0.5-0.3382612127 j =...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2197378

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Let DE be 1 unit. AC = 4 units. Area ABC is; 8sin60 = 4√(3) square units. a² = 1+2²-4cos45 a = 1.47362575821 units. (1.47362575821/sin45) = (1/sinb) b = 28.6750500631° c = 60-b c = 31.3249499369° d = 360--60-150  d = 150° e = 240-d e = 90° f² = 1²+1² f = √(2) units. g = 180-15-45-60 g = 60° h² = 4²+1.47362575821²-8*1.47362575821cos31.3249499369 h = 2.84622917461 units. (2.84622917461/sin31.3249499369) = (1.47362575821/sini) i = 15.61499741821° j = 60-i j = 44.38500258179° k = 120-j...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2197369

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Area Aqua, in square units to 2 d. p. is; Area triangle with two side 5 unit and 6 unit, and angle acos(0.2)° - Area triangle with two side 5 unit and 3.9332754507 unit, and angle 14.2804126089° - Area triangle with two side 3.9332754507 unit and 4.44921801671 unit, and angle (2*14.2804126089)° - Area triangle with two side 7 unit and 4.44921801671 unit, and angle 14.2804126089° - Area triangle with two side 1.53404004392 unit and 1.98043718084 unit, and angle (0.5acos(0.2))° = (0.5*5*6sin(a...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2195528

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Let length AB be 3 unit. Therefore; AC = 20 unit. It implies; Area large square is; 20² = 40 square unit. Area orange is; Area triangle with two side 17 unit and 32.0319709782 unit, and angle (180-atan(10/7))° + Area triangle with two side 20 unit and 44.0408623507 unit, and angle 53.4269678346° - Area square with side 20 unit + Area triangle with height 3 unit and base 4.2857142857 unit. = (0.5*32.0319709782*17sin(180-atan(10/7))) + (0.5*44.0408623507*20sin53.4269678346) - 20² + (0.5*4.2...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2193352

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Let the side of the square be 2 unit. Therefore; Area square is; 2² = 4 square unit. Area S is; Area triangle with two side 0.98921899145 unit and 1.02554900641 unit, and angle 14.318078177° - Area sector with radius 2 unit and angle 28.6361563539° + Area triangle with two side 2 unit each, and angle 28.6361563539° (0.5*0.98921899145*1.02554900641sin14.318078177) - (28.6361563539*2²π÷360) + (0.5*2²sin28.6361563539) = 0.12544441261 - 0.99959042698 + 0.95849162297 = 0.0843456086 space unit....

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2191627

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a² = 6²+3² a = √(45) a = 3√(5) units. a is the square side. tanb = (6/3) b = atan(2)° It implies; c = atan(½)° d² = (3√(5))²+(0.5(3√(5)))² d = (15/2) units. d is the radius of the arc. e = (atan(½)+atan(½))° e is the angle of the sector formed by the arc. tan(atan(½)) = f/(0.5*3√(5)) f = ¼(3√(5)) units. g = 3√(5)-¼(3√(5)) g = ¼(9√(5)) units. sin(atan(½)) = h/(¼(9√(5))) h = (9/4) units. cos(atan(½)) = j/(¼(9√(5))) j = (9/2) units. Therefore; Area Shaded exactly as a single fraction is...

Mathematics Question and Solution

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

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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/2190434

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Sir Mike Ambrose is the author of the question. Area green total, in square unit decimal form is; Area triangle with height 6sin(atan(3/5)) unit and base 6cos(atan(3/5)) unit + Area triangle with height 4 unit and base 4tan(atan(2/5)) unit. = ½*6sin(atan(3/5))*6cos(atan(3/5)) + ½*4*4tan(atan(2/5)) = 7.94117647059 + 3.2 = 11.1411764706 square unit. = 11.14 square units to 2 decimal places.

Mathematics Question and Solution

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

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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...
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