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Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2473184

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15² = a²+6² a² = 225-36 a = √(189) a = 3√(21) units. b = 2a b = 6√(21) units. sin75 = c/b c = 6√(21)sin74 c = 26.5585692881 units  d = 10+c d = 36.5585692881 units. cos75 = e/(6√(21)) e = 7.1163471929 units. sinf = 6/15 f = 23.5781784782° g = 75-f g = 51.4218215218° h = 180-2g h = 77.1563569564° j² = 2*15²-2*15²cos77.1563569564 j = 18.7074571083 units. k = 15-½(j) k = 5.6462714458 units. l = k+5+j-e l = 22.2373813613 units. m = j-e m = 18.7074571...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2460723

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Notice! (4+2√(3)) units = 7.4641016151 units is the side length of the regular hexagon. a = ⅙*180(6-2) a = ⅙(180*4) a = 120° a is the single interior angle of the regular hexagon. b = ½(a) b = ½(120) b = 60° c = b-45 c = 60-45 c = 15° d = 180-2c d = 180-2*15 d = 150° cos15 = (0.5(4+2√(3))/e e = 3.8637033052 units. f = ½(d) f = ½(150) f = 75° Let g be the side length of the inscribed congruent squares.  h = g-e h = (g-3.8637033052) units. Therefore;...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2456209

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Calculating angle EHB. Let the side length of the regular pentagon be 1 unit. Therefore; AB = BC = CD = DE = AE = 1 unit. a² = 2-2cos108 a = 1.6180339887 units. a is BE, the square side length. b = 108-½(180-108) b = 108-½(72) b =108-36 b = 72° b is angle BED c = 90-b c = 90-72  c = 18° c is angle DEG. sin18 = d/1 d = 1sin18 d = 0.3090169944 units. cos18 = e/1 e = 1cos18 e = 0.9510565163 units. f = a-e f = 1.6180339887-0.9510565163 f = 0.6669774724 unit...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2421406

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a² = 30²+10²-2*30*10cos120 a = 36.0555127546 cm. (36.0555127546sin120) = (30/sinb) b = 46.1021137521° cosb = 10/d Where d is PQ. cos46.1021137521 = 10/d d = 10/cos46.1021137521 d = 14.4222051019 cm.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2406880

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a = ⅕(180(5-2)) a = 108° b = 180-108 b = 72° sin72 = c/6 c = 5.7063390978 cm. cos72 = d/6 d = 1.8541019662 cm. e = 1.8541019662+6 e = 7.8541019662 cm f² = 7.8541019662²+6²-2*7.8541019662*6cos108 f = 11.2610625384 cm. (11.2610625384/sin108) = (6/sing) g = 30.4463843172° h = 90-30.4463843172 h = 59.5536156828° i = 180-18-59.5536156828 i = 102.4463843172° (5.7063390978/sin102.4463843172) = (j/sin59.5536156828) j = 5.0378552605 cm. k² = 6²+6²-2*6*6cos108 k = 9.7082039325 cm. l = 90-18 l...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2397700

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a² = 6²+8²-2*6*8cos30 a = 4.10628314132 cm. a = DE. (4.10628314132/sin30) = (8/sinb) b = 103.06431342951° b = Angle ADE. Angle AED = 180-30-103.06431342951  = 46.93568657049° tan30 = c/6 c = 3.46410161514 cm. c = CH. d = 8-2*3.46410161514  d = 1.07179676972 cm. e = 1.07179676972+3.46410161514 e = 4.53589838486 cm. f = atan(6/4.53589838486)  f = 52.91133691903° g = 90-52.91133691903  g = 37.08866308097° h = 37.08866308097-30 h = 7.08866308097° i = 60+46.93568657049 i = 106.93568657049°...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2373159

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a+a+b = 20  2a+b = 20 --- (1). 20² = c²+10² c² = 400-100 c = = √(300) c = 10√(3) units. It implies; a+b = c a+b = 10√(3) --- (2). Solve (1) and (2) simultaneously, Calculating a and b. dSubtracting (2) from (1). 2a+b = 20 -- (1) a+b = 10√(3) -- (2) a = 20-10√(3) a = 2.6794919243 units. It implies; From (2). a+b = 10√(3) b = 10√(3)-a b = 10√(3)-2.6794919243 b = 14.6410161514 units. It implies; Area Blue is; Area square with diagonal 14.6410161514 uni...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2366566

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Calculating red length. Observing Cosine Rule. a² = 8²+12²-2*8*12cos40 a = 7.8050923711 units. a is BD, the red length. Observing Sine Rule. (7.8050923711/sin40) = (12/sinb) b = 81.2114041855° b is angle ADC. c+70+81.2114041855 = 180 c = 28.7885958145° c is angle CAD. It implies; Green Length is; Again, Observing Sine Rule. (8/sin28.7885958145) = (d/sin70) d = 15.6101847422 units. Therefore; Green Length ÷ Red Length = 15.6101847422÷7.8050923711 = 2

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2364184

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Let the side of the inscribed square be a. Calculating a. tan60 = a/b √(3) = a/b b = a/√(3) units. It implies; b+b+a = 10 2(a/√(3))+a = 10 ⅓(2√(3)a)+a = 10 2√(3)a+3a = 30 (2√(3)+3)a = 30 a = 30/(2√(3)+3) units. a = 4.6410161514 units. c = ½(a) c = ½(30/(2√(3)+3)) c = (15/(2√(3)+3)) units. c = 2.3205080757 units. It implies; b = a/√(3) b = 4.6410161514/√(3) b = 2.6794919243 units. d = a+b d = 4.6410161514+2.6794919243 d = 7.3205080757 units. Therefore, the required angle, x is; tany =...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2361212

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Let the inscribed square side be a. tan60 = a/b a = √(3)b cm. Where b is BS = CR It implies; b+√(3)b+b = 10 (2+√(3))b = 10 b = 10(2-√(3)) cm. Therefore; a = √(3)*10(2-√(3)) a = 10(2√(3)-3) cm. a = 4.64101615138 cm. sin60 = 10(2√(3)-3)/c c = 20(2-√(3)) cm. Where c is CQ. d² = 10²+(10(2-√(3)))²-20*10(2-√(3))cos60 d = 8.96575472168 cm. Where d is AS. (8.96575472168/sin60) = (10(2-√(3))/sine) e = 15° Where e is angle PAS. f = 180-60-15 f = 105° Where f is angle BSA. g = 105-90 g = 15° Whe...
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