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Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2114980

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Sir Mike Ambrose is the author of the question. Let the side length of the regular hexagon be 1 unit. Area Hexagon is; (½(6))(1/(2tan(180/6))) = 3/2tan(30) = ½(3√(3)) square units. Notice; 1/sin105 = x/sin45 x = √(3)-1 unit. y = 1.23931367493 units. z = 1.50597117915 units. a = 120-asin(0.81811048221) a = 65.10390936101° c = 54.89609063899° d = 1.10874112934 units. Area Red is; Area triangle with height 1.10874112934 units and base sin60 units. = ½*1.10874112934sin60 = (26725571√(...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2108235

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Sir Mike Ambrose is the author of the question. Let the radius of the semicircle be 1 unit. Area Semicircle is; ½*1²*π 0.5π square units. Calculating AC = AB = BC sin67.5 = (AC)/1 AC = sin67.5 units. 1=a²+1-2acos82.5 a = 0.26105238444 units. b = AC - a b = 0.66282714807 unit. c = √(0.26105238444²(sin67.5)²-2*0.26105238444sin67.5*cos60) c= 0.82493683584 units. d = asin(0.26105238444sin60/0.82493683584) d = 15.90570135267° e = 60-d e = 44.09429864733° f = 0.650107 unit. g = 0.576911...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2054357

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Sir Mike Ambrose is the author of the question. Let the radius of the ascribed quarter circle be 2 units. Area Quadrant is; ¼(4)π = π square units. The radius, r of the congruent inscribed semi-circles is; 2r+√(3)r = 2 r = 2/(2+√(3)) units. r = 0.53589838486 units. a = 2r a = 1.07179676972 units. b² = 1.07179676972²+0.53589838486²-0.53589838486*2*1.07179676972cos150 b = 1.55909609015 units. (1.55909609015/sin150) = (1.07179676972/sinc) c = 20.10390936081° d = 45-c  d = 24.89609063919...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2034047

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EG = 3AG Let AG = 1 unit. Therefore; EG = 3 units. The side length of the regular pentagon is; AG+EG = 1+3 = 4 units. AE = 4 units. It implies, Area Blue is; 0.5*2*4sin108 = 4sin108 = 3.80422606518 square units. Calculating Area Green. (DG)² = 3²+4²-2*3*4cos108 DG = 5.6935408899 units. It implies; 5.6935408899² = 2(GH)² (GH)² = 0.5(5.6935408899)² (GH)² = 16.20820393248 square units.  Area Green= ½(GH)² = 0.5*16.20820393248  = 8.10410196624 square units. Therefore; Area Blue ÷ Area G...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2017107

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sin60 = a/20 a = 10√(3) cm. a+b = 20 b = (20-10√(3)) cm. c = 20-2b c = 20-2(20-10√(3)) c = 20-40+20√(3) c = (20√(3)-20) cm.  c = 14.64101615138 cm. Therefore; Shaded Area Red is; ½(14.64101615138)²+4((30π*20*20/360)-(½*20*20sin30)) = 107.17967697245+4(104.71975511966-100) = 107.17967697245+4*4.71975511966 = 126.05869745109 cm²

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2010957

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Let the a side length of the yellow regular triangle be 2 units. Therefore, a side length of the regular pentagon is 2 units. Area Yellow is; 0.5*2*2sin60 = 2sin60 = √(3) square units. = 1.73205080757 square units. Calculating r, radius of the circle. a = 108+0.5*60 a = 108+30 a = 138° cos30 = 1/b b = 1.15470053838 units. r² = 2²+1.15470053838²-2*2*1.15470053838cos138 r = 2.96070468869 units. (2.96070468869/sin138) = (1.15470053838/sinc) c = 15.12743321513° d = 180-108-15.12743321513...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2006913

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Let AB equal 1 unit. (1/sin60) = (a/sin20) a = 0.39493084363 units. a is BC. (1/sin60) = (b/sin100) b = 1.1371580426 units. b is AC. (1.1371580426/sin110) = (c/sin10) c = 0.21013831273 units. c is CD. (BD)² = 0.21013831273²+0.39493084363²-2*0.21013831273*0.39493084363cos120 BD = 0.53208888623 units. (0.53208888623/sin120) = (0.21013831273/sind) d = 20° d is angle CBD. Therefore the required angle x is; 100-d x = 100-20 x = 80°

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/1997583

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Notice; a² = 5² - (⅕(√(481)))² a = ⅕(12) units. b = 5-a b = ⅕(13) units. c² = 4²-(⅕(12))² c = ⅕(16) units. d = atan(4/3)° (a) Area A exactly is; ½*⅕(16)*(5+⅕(13)) - atan(4/3)π*16/360 = ((8*38)/25) - (2atan(4/3)π/45) = (304/25) - ((2atan(4/3)π)/45) = (2736-10πatan(4/3))/225 square units. = 4.74163825599 square units. (b) Calculating Area B to 2 decimal places. ½*10(10+5) - ½*⅕(16)(5+⅕(13)) - ((atan½+ata¾)π*16/360) - (⅕(13)*⅕(34-√(481))) - ½*⅕(√(481))(5+⅕(13)) - ((atan(12/√(481))+(2t...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/1993663

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Notice; Hexagon Area = 24√(3) square units. Calculating hexagon side length. Let it be a. (6a²)/(4tan30) = 24√(3) ½(3√(3))a² = 24√(3) 3a² = 48 a = 4 units. Equation of the curve is; y = ½(x²) ------ (1). sin60 = b/4 b = 2√(3) units. cos60 = c/4 c = 2 units. Gradient = ((4√(3)+2)-(2√(3)+2))/(2-4) Gradient = -√(3) (y-(4√(3)+2))/(x-2) = -√(3) y = -√(3)x+6√(3)+2 ---- (2). Equation (1) and (2). ½(x)² = -√(3)x+6√(3)+2 x = 3.53906 y = ½(3.53906)² y = 6.2624728418 d = 2(3.53906) d = 7....

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/1985499

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AE = CF = (12√(2)-12) cm. AE = CF = 4.97056274848 cm. EF = 12√(2)-2(4.97056274848) EF = 7.02943725152 cm. sin60 = a/7.02943725152 a = 6.08767123412 cm. a = height of triangle EFG. It implies; Length BG is; 6√(2)-6.08767123412  = 2.39761014012 cm.
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