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Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2758862

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13² = 20²+11²-2*20*11cosa 169 = 521-440cosa 440cosa = 521-169 cosa = 352/440 a = 36.8698976458° (13/sin36.8698976458) = (11/sinb) b = 30.5102374061° c = 180-a-b c = 112.6198649481° d = 90-a d = 53.1301023542° e = c-d e = 59.4897625939° cos53.1301023542 = f/11 f = 6.6 units. cos59.4897625939 = g/6.6 g = 3.3507692308 units. sin59.4897625939 = h/6.6 h = 5.6861538462 units. Therefore, area red is; 0.5gh = 0.5*3.3507692308*5.6861538462 = 9.5264946746 square...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2755522

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Sir Mike Ambrose is the author of the question. Let the side length of the square be 10 units. Area square is; 10² = 100 square units. Therefore; Area R is; Area semi circle with radius 5 units - Area sector with radius 5 units and angle (180-2atan(2))° - Area kite with diagonal lengths √(10²+5²) units and √(200-200cos(2atan(½))) units + Area sector with radius 10 units and angle 2atan(½)° - 2(area quarter circle with radius 5 units - area triangle with height and base 5 unit...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2754168

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Calculating green area. c² = a²+b² c = √(4²+6²) c = √(52) c = 2√(13) units.  c = 7.2111025509 units. d = 90-atan(4/6) d = atan(3/2)° e = 180-2d e = (180-2ata(3/2))° sin(0.5(180-2ata(3/2))) = (0.5*2√(13))/f f = 6.5 units. f is the radius of the half circle. g = 180-2(180-2atan(3/2)) g = 180-360+4atan(3/2) g = (4atan(3/2)-180) g = 45.2397298961° Therefore, green area is; Area sector with radius 6.5 units and angle 45.2397298961° - Area triangle with height 6.5sin...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2750835

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Shaded area is; Area sector with radius 10 units and angle acos(0.7) - Area triangle with height √(51) units and base 7 units - area sector with radius 3 units and angle 81.37307344° - area sector with radius 10 units and angle 17.2538531174° + area triangle with two side length 10 units, and angle 17.2538531174° = (acos(0.7)*1))π÷360) - ½(√(51)*7) - (9π*81.37307344)/360 -(100π*17.2538531174)/360 + ½(100)sin17.2538531174 = 39.7699415092 - 24.9949994999 - 6.39102624298 - 15.0568272777 +...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2749450

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a²+8² = 10² a = 6 units. a is AC,the height of triangle ABC. Calculating b, radius of the inscribed circle. 10b+8b+6b = 8*6 24b = 48 b = 2 units. c = 6-b c = 4 units. d = 8-b d = 6 units. e = 10-d e = 4 units. tanf = 8/6 f = atan(4/3)° Therefore, area red is; Area triangle with height 6 units and base 8 units - Area triangle with height 4 units and base 4sin(atan(4/3)) units. ½(6*8)-½(4*4sin(atan(4/3))) = 24-8(4/5) = ⅕(120-32) = ⅕(88) square units. = 17....

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2738459

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Let k = 1 unit. a = 5+1 a= 6 units. a is the side length of the square. b = ½(a) b = 3 units. c = b-1 c = 2 units. tand = 6/2 d = atan(3)° e = (180-atan(3))° It implies; (3/sin(180-atan(3))) = (1/sinf) f = 18.4349488229° g = 180-(180-atan(3))-f g = 53.1301023542° h = 90-g h = 36.8698976458° j² = 3²+6²-2*3*6cos36.8698976458 j = 4.0249223595 units. (6/sink) = (4.0249223595/sin36.8698976458) o = 63.4349488229° l = 180-63.4349488229 l = 116.565051177...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2730809

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Area red is; Area semi circle with radius 5 cm - Area sector with radius 5 cm and angle (180-2atan(2))° - Area kite with diagonal lengths √(10²+5²) cm and √(200-200cos(2atan(½))) cm + Area sector with radius 10 cm and angle 2atan(½)° - 2(area quarter circle with radius 5 cm - area triangle with height and base 5 cm respectively). = 12.5π - 11.591190225 - 50 + 46.3647608999 - 14.2699081699 = 9.77357067487 cm²

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2730371

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Sir Mike Ambrose is the author of the question. Area blue is; Area triangle with side 8.81712800181 cm and 7.80776406404 cm, and angle 19.3341412463° = ½(8.81712800181*7.80776406404)sin19.3341412463 = 11.3960010284 ≈ 11.40 cm²

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2728922

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Sir Mike Ambrose is the author of the question. Area purple exactly in square cm decimal form is; Area triangle with side 17.1220111351 cm and 15.6524758425 cm, and angle 75.963756532° - Area triangle with side 3.28886874952 cm and 2.857142857 cm, and angle 8.1301023539° + Area triangle with side 2.857142857 and 2.82842712466 cm, and angle 8.1301023539°  = ½(17.1220111351*15.6524758425)sin75.963756532 - ½(3.28886874952*2.857142857)sin8.1301023539 + ½(2.857142857*2.82842712466)sin8.1301...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2726967

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Let a be 1 unit. d = ⅙*180(6-2) d = 120° d is the single interior angle of the regular hexagon. cos60 = e/1 e = 0.5 units. f = a+2e f = 2 units. f is CF. g² = 0.5²+2²-2*0.5*2cos60 g = 1.8027756377 units. g is MF. (1.8027756377/sin60) = (0.5/sinh) h = 13.897886248° h is angle CFM. j = 60-h j = 46.102113752° j is angle EFN. k = ½(g) k = 0.9013878189 units. k is FN = MN. Calculating b. b² = 0.9013878189²+1²-2*0.9013878189*1cos46.102113752 b = 0.75 units....
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