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Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/1965364

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a² = 5²+12² a = 13 cm. a = AC = BD = diameter of the ascribed circle. b = ½(13) b = 6.5 cm. b = OG = OE = radius of the ascribed circle. c = atan(6/(6.5+2.5)) c = atan(6/9) c = 33.69006752598° c = Angle OEF = Angle BCF. d = 6.5-2.5 d = 4 cm. tan33.69006752598 = e/4 e = 8/3 cm. f = atan((8/3)/(5/2)) f = 46.84761026599° g = atan(2.5/6) g = 22.61986494804° h = 90-22.61986494804-46.84761026599 h = 20.53252478597° h = Angle BOG. i = ½(180-20.53252478597) i = 79.73373760702° i = Angle OGB =...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/1958336

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a² = 10²+16²-2*10*16cos120 a = 2√(129) units. Where a is length AC. (3√(129)/sin120) = (16/sinb) b = 37.58908946897° c = 90-b c = 52.41091053103°  d = 60-b d = 22.41091053103° e = 90-d e = 67.58908946897°  f = 90-60 f = 30° cos37.58908946897 = g/10 g = 7.92405815693 units. i = 30+37.58908946897 i = 67.58908946897° tan67.58908946897 = j/7.92405815693 j = 19.2148198619 units. Where j is the radius of the arc. sin67.58908946897 = 19.2148198619/k k = 20.78460969082 units. l² = (2√(129)...

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/1952000

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a² = 15²+12²-2*12*15cos120 a = 23.43074902772 cm. Where a is the side length of the equilateral triangle ABC. (23.43074902772/sin120) = (12/sinb) b = 26.32950349168° c = 60-b c = 33.67049650832° d² = 15²+15²-2*15*15cos120 d = 25.98076211353 cm. e = atan(7.5/25.98076211353) e = 16.10211375199° f = 90-e f = 73.89788624801° g = 180-f-c g = 72.43161724367° (15/sin72.43161724367) = (h/sin73.89788624801) h = 15.11661227595 cm. i = a-h  i = 8.31413675177 cm. Let the radius of the green ins...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/1935082

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Let the side of the regular pentagon be 1 unit. a = 108-90 a = 18° b = 180-108-18 b = 54° (1/sin54) = (c/sin108) c = 1.17557050458 units. (1/sin54) = (d/sin18) d = 0.38196601125 unit. e = 1-d e = 0.61803398875 unit. f² = 0.61803398875²+1²-2*0.61803398875cos108 f = 1.3281310261 units. (1.3281310261/sin108) = (1/sing) g = 45.73230144788° h = 180-108-45.73230144788 h = 26.26769855212°  I = 180-72-45.73230144788 i = 62.26769855212° (0.61803398875/sin62.2676...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/1930117

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a² = 3²+4² a = 5 cm. Where a is AC. b = atan(4/3)° Where b is angle DAC. c = 60+atan(4/3) c = 113.13010235416° Where c is angle EAC. d² = 3²+5²-2*3*5cos113.13010235416 d = 6.76643256752 cm. Where d is CE. (6.76643256752/sin113.13010235416) = (3/sine) e = 24.06202137986° Where e is angle ACF. f = atan(3/4)-24.06202137986  f = 12.80787626598 cm. Where f is angle DCE. tan(12.80787626598) = g/4 g = 0.90935597101 cm. Where g is DF. cos12.80787626598 = 4/h h = 4.10206390516 cm. Where h is CF....

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/1920365

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a = 45-atan(3/4) a = 45-36.86989764584  a = 8.13010235416° Where a is angle DCF. b² = 2(5²) b = 5√(2) cm. Where b is CF = AE. c² = (5√(2))²+4²-10√(2)*4cos8.13010235416   c = 3.16227766017 cm. Where c is DF. (4/sind) = (3.16227766017/sin8.13010235416) d = 10.30484646877° Where d is angle DFC. e = 45-10.30484646877  e = 34.69515353123° Where e is angle AFD. tan34.69515353123 = f/5 f = 3.46153846154 cm. g = 90-34.69515353123 g = 55.30484646877° h = atan(5/(5-3.46153846154)) h = 72.89727103...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/1919356

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Notice; Triangle ABC is equilateral. Let the side of the regular pentagon be a. Single interior angle of the regular pentagon is; ⅕(180*3) = 108° (HF)² = 2a²-2a²cos108 HF = 1.61803398875a units. sin18 = b/a b = 0.30901699437a units. c = HF-b c = 1.61803398875a-0.30901699437a c = 1.30901699438a units. d = 1-c d = (1-1.30901699438a) units. cos18 =e/a e = 0.9510565163a units. Calculating a, side length of the regular pentagon. tan60 = e/d √(3) = 0.9510565163a/(1-1.30901699438a) √(3)-2.26...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/1904531

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Radius of the circle r, is; πr² = 25π r = 5 cm. Therefore diameter is; 2r = 10 cm. Let the side of the small yellow Inscribed square be x. a² = 2x² a = √(2)x cm. Where a is a diagonal of the small yellow Inscribed square. Extending a. We now have a rectangle inscribed the circle (cyclic quadrilateral) with diameter 10 cm. Where 6 cm is the width and (6+√(2)x) cm is the length. Calculating x (small yellow Inscribed square length) 10² = 6²+(6+√(2)x)² 100-36 = (6+√(2)x)² 8 = 6+√(2)x 2 = √...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/1896554

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AP = √(20²+10²) AP = √(500) AP = 10√(5) cm. OA (radius of the semi circle) is: ½(AP) = 5√(5) cm. tana = 20/10 a = atan(2)° Where a is angle MAO = angle AMO. b = (180-2atan(2))° Where b is angle OMN = angle ONM. c = 180-2b c = 180-2(180-2atan(2)) c = 4atan(2)-180 c = 73.73979529169° Where c is angle MON. sin(0.5*73.73979529169) = d/(5√(5)) d = 3√(5) cm. Where d is half MN. MN = 2d MN = 6√(5) cm. It implies; Area Blue, Area Triangle DMN is; 0.5*10*6√(5)...
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