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Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2144034

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

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2139607

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Let O be the centre of the circle. Since AE = EB, therefore E is the midpoint of length AB. AB = 10cm, therefore AE = EB = 10/2 = 5cm. r will be; Triangle EBC Area+Triangle EOC Area+Triangle AOE Area+Triangle AOD Area+Triangle DOC Area = Square ABCD Area. The triangles height and base. EBC, height=5cm, base=10cm. EOC, height=rcm, base=√(5²+10²)=√(125)=5√(5)cm. AOE, height=(10-r)cm, base=5cm. AOD, height=rcm, base=10cm. DOC, height=rcm, base=10cm. Therefore r is; (5x10)/2+(5√(5)r)/2+(5(1...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2126302

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100 = 49+64-2*7*8cosA 112cosA = 113-100 A = acos(13/112) A = 83.3345727438° (7/cosB) = (10/cos83.3345727438) B = 44.0486256741° (8/cosC) = (10/cos83.3345727438) C = 52.6168015821° a²= 2.5²+10²-20*2.5cos52.6168015821 a= 8.7116506555 cm. (8.7116506555/sin52.6168015821) = (2.5/sinb) b = 13.1808743912° (b1)² = 2.5²+10²-20*2.5cos44.0486256741 b1 = 8.3852549156 cm. (8.3852549156/sin44.0486256741) = (2.5/sinc) c = 11.9635307444° d = 180-11.9635307444-13.1808743912 d = 1...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2120814

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a² = 6²+18²-2*6*18cos150 a = 23.3893455919 cm. (23.3893455919/sin150) = (18/sinb) b = 22.6307402124° tan22.6307402124 = c/6 c = 2.5013366786 cm. Area Red exactly in decimal is; 0.5*2.5013366786*18sin60 = 19.4959899641 cm² Calculating Tanx. d² = 6²+18² d = 6√(10) cm. d = 18.973665961 cm. e² = 6²+2.5013366786² e = 6.5005142243 cm. f = 18-2.5013366786 f = 15.4986633214 cm. 15.4986633214² = 6.5005142243²+18.973665961²-2*6.5005142243*18.973665961cosg 240.2085647501 = 402.2566851799-246.67...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2120575

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sin30 = a/10 a = 5 cm. b = 10+2a b = 20 cm. c² = 20²+4²-160cos60 c = 4√(21) cm. c = 18.3303027798 cm. (18.3303027798/sin60) = (20/sind) d = asin(5√(7)/14)° d = 70.8933946491° e = 180-d e = (180-asin(5√(7)/14))° e = 109.1066053509° Where e is x. Therefore; tanx is; tan(180-asin(5√(7)/14)) tan(109.1066053509) = -2.8867513459 Calculating Blue Area. f² = 10²+10²-200cos 120 f = 10√(3) cm. g² = 10²+4²-2*10*4cos120 g = 2√(39) cm. (2√(39)/sin120) = (10/sinh) h = asin(5√(13)/26)° h = 43.897886...

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/2078804

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Let the side length of the congruent yellow regular hexagon be 1 unit. a = 3sin30+1 a = 2.5 units. sin60 = b/1 b = 0.5√(3) units. c² = a²+b² c² = 2.5²+(0.5√(3))² c = √(7) units. c = 2.64575131106 units. c is the radius of the circle. d² = √(7)²-1 d = √(6) units. e = d-b e = √(6)-0.5√(3) e = 1.583464339 units. e is the height of the green inscribed triangle. Area Green Triangle is; Half the height, 1.583464339 units multiply the base, 1 unit of the triangle = 0.5*1.583464339*1 = 0.791732...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2069018

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Sir Mike Ambrose is the author of the question. a² = 8²+12²-2*8*12cos60 a = 4√(7) cm. b = 2a b = 8√(7) cm. (4√(7)/sin60) = (8/sinc) c = 40.89339464928° (16/sin40.89339464928) = (8√(7)/Sind) d = 60° e² = 12²+16²-2*12*16cos60 e = 4√(13) cm. (a) Let beta be x. Calculating tanx. (12/sinx) = (4√(13)/sin60) x = asin(3√(39)/26) It implies; tanx is; tan(asin(3√(39)/26)) = ⅕(3√(3)) (b) Calculating Orange hi Area. f² = 6²+8²-2*6*8cos60 f = 2√(13) cm. g² = 8²+24²-2*8*24cos60 g = 8√(7) cm. (8/...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2064854

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Calculating x. ½(x+2)(x-2) = 30 x²-4 = 60 x² = 64 x = 8 m. Therefore; AB = 8-2 = 6 m. BC = 8+2 = 10 m. It implies; L² = 6²+10² L² = 36+100 L² = 136 L = √(136) L = √(2*2*34) L = 2√(34) m.
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