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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/1996244

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Let the radius R, of the half circle be 1 unit. sin30 = c/1 c = ½ units. c = 0.5 units. cos30 = d/1 d = ½√(3) units. d = 0.86602540378 units. e = 1-0.86602540378  e = 0.13397459622 units. f² = (0.13397459622)²+(0.5)² f = 0.51763809021 units. Calculating r, radius of the small inscribed yellow circle. Considering similar triangle ratios. 0.51763809021 = (1-r) 0.5 = (0.5+r) Cross Multiply. 0.5-0.5r = 0.51763809021r+0.2588190451  0.5-0.2588190451 = 0.5r+0.51763809...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/1988595

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Let BD be 1 unit. Therefore; (1/sin100) = (d/sin70) d = 0.95418889414 units. (1/sin80) = (AB/sin70) AB = 0.95418889414 units. AB is c. It implies; d = c. Calculating a. (a/sin20) = (0.95418889414/sin80) a = 0.33138632523 units. Calculating b. (1/sin100) = (e/sin10) e = 0.17632698071 units. (0.17632698071/sin30) = (f/sin110) f = 0.33138632523 units. It implies; (0.33138632523/sin20) = (b/sin140) b = 0.6228025689 units. Confirming the proof; a+b = c Notice; c = 0.95418889414 units...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/1982892

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Let the radius of the large circle be 1 unit. Diameter of the large circle = 2 units. sin60 = 2/a a = ⅓(4√(3)) units. Where a is the side length of triangle ABC. b² = 2-2cos b = √(3) units. c = a-b c = ⅓(√(3)) units. (d/sin50) = (4√(3)/(3sin100)) d = 1.79639514045 units. e² = (⅓(2√(3)))²+1² e = ⅓√(21) units. 1² = (⅓√(21))²+f²-2*⅓√(21)f cos(atan(3/(2√(3))-10) f² - 2.62161244054f + 1.33333333333 = 0  f = 1.93113 units. g² = 1.93119²+(⅓(4√(3)))²-2*1.93119(⅓(4√(3)))cos10 g = 0.5277832777...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/1978112

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a² = 2*12²-2*12²cos120 a = 12√(3) cm. a = 20.78460969083 cm. a = AB. b = 2a b = 24√(3) cm. b = 41.56921938165 cm. b = AC. c² = 12²+41.56921938165²-24*41.56921938165cos30 c = 31.74901573277 cm. c = CO1 (31.74901573277/sin30) = (12/sind) d = 10.89339464913° d = Angle O1CA. e = 180-10.89339464913-30 e = 139.10660535087° e = Angle AO1C. f = asin(12/31.74901573277)  f = 22.2076542986° f = Angle O1CD. cos22.2076542986 = g/31.74901573277 g = 29.39387691339 cm. g = CD. h = 2*10.89339464913 h =...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/1971670

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Notice; AB = 25 units. cos30 = 8√(3)/a a = 16 units. tan30 = b/(8√(3)) b = 8 units. Let the side of the regular hexagon be c. c = ¼(AC) Calculating AC. ((AC)/sin46) = (25/sin74) AC = 18.70821971213 units. c = ¼(18.70821971213) c = 4.67705492803 units. Calculating r, radius of the circle. (r/sin16) = (25/sin148) r = 13.00374294827 units. Calculating Shaded Area. cos30 = d/4.67705492803 d = 4.05044838257 units. e = 2d e = 8.10089676514 units. tan16 = f/(0.5*25) f = 3.58431732199 uni...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/1967906

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Calculating r, radius of the circle. (r/tan40)+(r/tan30) = 10 r = 3.42020143326 cm. (a/sin60) = (10/sin40) a = 13.47296355334 cm. tan40 = 3.42020143326/b b = 4.07603734548  (4.07603734548/sin50) = (c/sin80) c = 5.24005260459 cm. d = 13.47296355334-4.07603734548 d = 9.39692620786 cm. e² = 9.39692620786²+5.24005260459²-2*9.39692620786*5.24005260459cos130 e = 13.38142726359 cm. (13.38142726359/sin130) = (5.24005260459/sinf) f = 17.45618925878° g = 100-17.45618925878  g = 82.54381074122°...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/1956220

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a = atan(6/12) a = 26.56505117708° a = Angle BAE. b = 45-26.56505117708 b = 18.43494882292° b = Angle CAE. d = ½√(2*12²) d = 6√(2) cm. d = half AC = radius of the circle. Let the centre of the circle be O. e = 180-2(18.43494882292) e = 143.13010235416° e = Angle AOF. f² = 2*(6√(2))²-2*(6√(2))²cos143.13010235416 f = 16.099689438 cm. f = AF. g = 90-18.43494882292 g = 71.56505117708° g = Angle AFN. h = 180-71.56505117708-26.56505117708 h = 81.86989764584° h = Angle ANF. (16.099689438/sin8...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/1952625

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Let the square side, x be 1 unit. sin67.5 = a/1 a = 0.92387953251 units. cos67.5 = b/1 b = 0.38268343237 units. c = 2b c = 0.76536686473 units. d² = 1²+1² d = √(2) units. sin67.5 = e/√(2) e = 1.30656296488 units. e is the radius of the half circle. f = e-c f = 1.30656296488-0.76536686473 f = 0.54119610015 units. g = r-b g = (r-0.38268343237) units. r² = (r-0.38268343237)²+h² h² = r²-r²+0.76536686474r-0.14644660941 h² = 0.76536686474r-0.14644660941 h = √(0...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/1949823

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Let AB be 1 unit. (1/sin100) = (b/sin30) b = 0.50771330594 units. (1/sin110) = (d/sin30) d = 0.53208888624 units. d is CB. (0.50771330594/sin30) = (c/sin50) c = 0.77786191343 units. a² = 0.77786191343²+0.53208888624²-2*0.77786191343*0.53208888624cos10 a = 0.27014860749 units. Therefore, showing that; c = a+b Again; a = 0.27014860749 units. b = 0.50771330594 units. c = 0.77786191343 units. It implies; a+ b = 0.27014860749+0.50771330594 = 0.77786191343 units, which is c. Showed!
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