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Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2009313

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Let the adjacent base and adjacent height of the triangle be 3 units each. a² = 2*3² a = 3√(2) units. b = ⅓(a) b = ⅓(3√(2))  b = √(2) units. c² = 2+9-6√(2)cos45 c = √(5) units. (√(5)/sin45) = (√(2)/sind) d = 26.56505117708° e = 45-26.56505117708  e = 18.43494882292° f = √(2)r units. Calculating r. r² =5+2r²-2√(5)*√(2)rcos18.43494882292  0 = r²+5-6r r²-6r+5 = 0 Therefore; Solving the quadratic equation. r ≠ 5 units. r = 1 unit. Calculating the alpha, the required angle. Let it be g....

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2009073

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Let AB = 1 unit. a² = 2-2cos108 a = 1.61803398875 units. a is AD. b = 108-36-18 b = 54° b is angle DAF. c = 108-36-30 c = 42° c is angle ADF. d = 180-54-42 d = 84° d is angle AFD. (1.61803398875/sin84) = (e/sin54) e = 1.31622742593 units. e is DF. (CF)² = 1.31622742593+1-2*1.31622742593cos30 CF = 0.6728163648 units. (0.6728163648/sin30) = (1.31622742593/sinf) f = 78° f is the supplementary angle of angle g. Calculating angle g. g+f = 180 g = 180-f g = 180-78 g = 102° g is angle DCF. T...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2008166

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Let the side length of the regular pentagon be 2 units. a² = 2²-1² a = √(3) units. b² = 5-4cos108 b = 2.49721204096 units. (2.49721204096/sin108) = (2/sinc) c = 49.61382244056° d = 90-c d = 40.38617755944° e² = 3+2.49721204096²-2√(3)*2.49721204096cos40.38617755944 e = 1.62694657231 units. (1.62694657231/sin40.38617755944) = (√(3)/sinf) f = 43.61382244075° g = 180-e-f g = 96° Let the radius of the inscribed circle be r. Calculating r. r(√(3)+1.62694657231+2.49721204096) = (1.6269465723...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2007601

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Let BC be 1 unit. tan60 = a/1 a = √(3) units. b² = √(3)²+1 b² = 4 b = 2 units. b is AB. Area Blue is; ½*1*√(3) = ½√(3) square units. Calculating Area Green. tanc = √(3)/(√(3)+1) c = atan(½(3-√(3)))° (½(3-√(3))) = d/1 d = ½(3-√(3)) units. e = (√(3)-1) units. tan30 = f/(√(3)-1) f = ⅓(3-√(3)) units. It implies; Area Green is; Area trapezoid with parallel sides (½(3-√(3))) units and √(3) units respectively, and height √(3) units - Area Blue - Area triangle with height (√(3)-1) units an...

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/2006521

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Notice; AE = BI = 5 units. BF = 3 units. a² = 8²+5² a = √(89) units. a is AB. √(89)² = b²+5² b = √(89-25) b = 8 units. b is DG. DH = 8-GH DH = 8-3 DH = 5 units. It implies, area x is; Area square ABCD - 2(Area triangle ADG) = √(89)² - 2(½*8*5) = 89-40 = 49 square units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2006438

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Let a be 1 unit. (1/sin9) = (b/sin36) b = 3.75738972957 units. (AB)² = 3.75738972957²+1-2*3.75738972957cos135 AB = 4.52014702134 units. (4.52014702134/sin135) = (f/sin18) f = 1.97537668119 units. (4.52014702134/sin135) = (e/sin27) e = 2.90211303259 units. Observing the proof. Notice; a = 1 unit. b = 3.75738972957 units. e = 2.90211303259 units. f = 1.97537668119 units. It implies; (e/a)-(b/f) = 1 (2.90211303259/1)-(3.75738972957/1.97537668119) = ? 2.90211303259-1.90211303259 = 1 Pro...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2006083

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Let the side length of the three congruent squares be 1 unit. Area Orange is; 1² = 1 square units. Calculating Area Blue. a² = 1+2² a = √(5) units. ⅓ = b/1 b = ⅓ units. c = 1+⅓ c = (4/3) units. cos(tan(½)) = d/(4/3) d = (8√(5)/15) units. d = 1.192569588 units. e = √(5)-(8√(5)/15) e = (7√(5)/15) units. e = 1.0434983895 units. cos(atan(½)) = (7√(5)/15)/f f = (7/6) units. tan(atan(½)) = g/(7√(5)/15) ½ = g/(7√(5)/15) g = ½(7√(5)/15) units. h = atan(½)°...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2005789

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Let the square side be 2a units. b² = (2a)²+a² b = √(5a²) b = √(5)a units. cos(atan(½)) = c/a c = ⅕(2√(5))a unit. d = b-c d = √(5)a-⅕(2√(5))a d = ⅕(3√(5))a units. Calculating a. 1 = a²+ (⅕(3√(5))a)²-2a(⅕(3√(5))a)cos(180-atan(2)) 1 = (14a²/5)+(6a²/5) 14a²+6a² = 5 20a² = 5 a = ½ units. 2a (the square side length) = 1 unit. (1/sin(180-atan2)) = (0.5/sine) e = 26.56505117708° f = 180-(180-atan(2))-26.56505117708  f = 36.86989764584° g = 90-36.86989764584 g = 53.13010235416°  h = atan(2)°...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2005668

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Let s be 4 units. It implies; r = ¼(5*4) r = 5 units. a² = 32-32cos108 a = 6.472135955 units. b = ½(a) b = 3.2360679775 units. Notice; Angle BGC = 36° cos18 = c/4 c = 3.80422606518 units. sin18 = d/4 d = 1.2360679775 units. tan36 = 3.80422606518/e e = 5.2360679775 units. Calculating BG. BG = d+e BG = 1.2360679775+5.2360679775 BG = 6.472135955 units. Area Green plus Area Blue is; 0.5*6.472135955*6.472135955sin36 = 12.3107341487 square units. Let x and y be BF and FG respectively. T...
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