Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2012023

Area Shaded exactly in square units as a single fraction is; Area triangle with height 6√(3) units and base 6 units - Area triangle with height 2√(3) units and base 2 units - Area sector with radius 2 units and angle 120° - Area sector with radius 6 units and angle 60° = ½*6√(3)*6 - ½*2√(3)*2 - (120π*4/360) - (60π*36/360) = 18√(3) - 2√(3) - ⅓(4π) - 6π = 16√(3) - ⅓(4π) - 6π = ⅓(48√(3)-4π-18π) = ⅓(48√(3)-22π) square units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2012019

Let the side of the equilateral triangle be 2 units. Let the side of the square be a. Calculating a. tan60 = a/1 a = √(3) units. Area square is; a² = √(3)² = 3 square units. Calculating area green. b² = 2√(3)² b = √(6) units. c = 180-60-45 c = 75° (√(3)/sin75) = (d/sin60) d = 1.55291427062 units. e = b-d e = 0.89657547217 units. (f/sin45) = (√(3)/sin75) f = 1.26794919243 units. (1.26794919243/sin45) = (0.89657547217/sing) g = 30° sin30 = h/(√(3)+1) h = ½(√(3)+1) units. Theref...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2011345

Let the shortest length of the composite plane shape be 1 unit. (1/sin12) = (a/sin153) a = 2.18357369878 units. (2.18357369878/sin27) = (b/sin99) b = 4.75051853365 units. c² = 4.75051853365+1-2*4.75051853365cos39 c = 4.02290116111 units. Calculating the required angle x. (4.02290116111/sin39) = (1/sinx) x = 9°

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2010957

Let the a side length of the yellow regular triangle be 2 units. Therefore, a side length of the regular pentagon is 2 units. Area Yellow is; 0.5*2*2sin60 = 2sin60 = √(3) square units. = 1.73205080757 square units. Calculating r, radius of the circle. a = 108+0.5*60 a = 108+30 a = 138° cos30 = 1/b b = 1.15470053838 units. r² = 2²+1.15470053838²-2*2*1.15470053838cos138 r = 2.96070468869 units. (2.96070468869/sin138) = (1.15470053838/sinc) c = 15.12743321513° d = 180-108-15.12743321513...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2010716

Notice; GH = 8 units. Calculating the side length of the regular pentagon. a = 108-90 a = 18° a is angle EFG. b = 180-108-18 b = 54° b is angle EGF. (8/sin108) = (c/sin18) c = 2.59935756986 units. c is EG. d = 90-54 d = 36° d is angle DGH. cos36 = 8/e e = 9.88854382 units. e is DG. Therefore the regular pentagon side length (DE) is; c+e = 2.59935756986+9.88854382 = 12.48790138986 units. f = ½(12.48790138986) f = 6.24395069493 units. f is AJ. tan36 = g/8 g = 5.81234022404 units. g is...

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Our certified, experienced, resilient, productive and committed Math Educators will be glad to be at your service. We make teaching and learning Mathematics fun for learners, we expose the simplicity and beauty of Mathematics to our learners, and mentor them to appreciate and love Mathematics. Communicate us to mentor/educate you Mathematics better online at affordable tuition. We are smart and clever.

Mathematics Question and Solution

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

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

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

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

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...

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