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Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2041198

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Sir Mike Ambrose is the author of the question. Notice; BC = 2 units. a = ⅛(180*6) a = 135° b = 2+2(2sin45) b = 4.82842712475 units. c = b+2 c = 6.82842712475 units. Let AB be d. Calculating d. d² = 6.82842712475²+2²-4*6.82842712475cos135 d = AB = 8.36308110071 units.  (a) (AB/BC)² exactly in decimal is; (8.36308110071/2)² = 17.48528137426  = 18095509063163401/1034899506381316 exactly in fraction. (b) Calculating green area. e = (2√(2)+2) units. f = (2√(2)+4) units. g = atan((2√(...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2041180

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Let the regular pentagon side be 1 unit. Let the width and length of the inscribed red rectangle be a and b respectively. (1/sin72) = (c/sin54) c = 0.85065080835 units. d = 180-54-108 d = 18° (d/sin18) = (0.85065080835/sin108) d = 0.27639320225 units. Calculating a. cos18 = a/0.27639320225 a = 0.26286555606 units. (e/sin54) = (0.85065080835/sin108) e = 0.72360679775 units. f = (0.72360679775-b) units. sin72 = g/1 g = 0.9510565163 units. h = 0.5g h = 0.47552825815 units. h is radius o...

We are smart and clever!

https://onlineedumath.com/update/we-are-smart-and-clever/2039299

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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/2039291

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Sir Mike Ambrose is the author of the question. tan30 = 1/a a = √(3) units. b = a-1 b = (√(3)-1) unit. It implies; Area Shaded in square units exactly as a single fraction is; Area triangle with height 1 unit and base (√(3)-1) unit + Area sector with radius 2 units and angle 30° - Area triangle with height √(3) units and base 1 unit. ½*1(√(3)-1) + (30*4π/360) - ½*1*√(3) = ½(√(3)-1)+⅓(π)-½(√(3)) = ⅓(π)-½ = ⅙(2π-3) square units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2039257

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Let the side length of the regular pentagon be 1 unit. z = √(2-2cos108) z = 1.61803398875 units. sin18 = y/1 y = 0.30901699437 units. cos18 = x/1 x = 0.9510565163 units. Area Regular Pentagon is; 0.5sin108+0.5*(1+1.61803398875)*0.9510565163 = 0.47552825815+1.24494914245 = 1.7204774006 square units. (1/sin54) = (a/sin18) a = 0.38196601125 units. b =1-0.38196601125  b = 0.61803398875 units. (1/sin54) = (c/sin108) c = 1.17557050458 units. sin36 = 0.61803398875/d d = 1.05146222424 units....

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2037332

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sina = 7/25 a = asin(7/25)° tan(asin(7/25)) = b/25 b = 7.29166666667 cm. c = 25-7.29166666667 c = 17.70833333333 cm. cos(asin(7/25)) = 25/d d = 25.96150997149 cm. (7/25) = e/17.70833333333 e = 4.95833333333 cm. It implies; DF = e+d DF = 4.95833333333+25.96150997149 DF = 30.91984330482 cm. DF ≈ 31 cm to the nearest whole number.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2037076

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Let the side length of the inscribed yellow square be 1 unit. Area yellow square is; 1² = 1 square unit. Side length of the small regular pentagon is 1 unit. a² = 2-2cos108 a = 1.61803398875 units. a is the side length of the big regular pentagon. b² = 1.61803398875²+1.61803398875²-2*1.61803398875*1.61803398875cos108 b = 2.61803398875 units. c = ½(2.61803398875-1) c = 0.80901699438 units. cos36 = 0.80901699438/e e = 1 unit sin36 = f/1 f = 0.58778525229 units. g = 1.61803398875-1 g = 0....

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2035754

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Sir Mike Ambrose is the author of the question. a² = 2²+2² a = 2√(2) units. 2b² = 4 b = √(2) units. c = 3-√(2) units. Let the side of the inscribed regular pentagon be d. Calculating d. e = ⅕(180*3) e = 108° f = ½(180-108) f = 36° (g/sin108) = (d/sin36) g = 1.61803398875d units. (1.61803398875d)² = (3-√(2))²+(d/2)²  d = 1.03050649521 units. Where d is the side length of the regular pentagon.  g = 1.61803398875d g = 1.61803398875*1.03050649521  g = 1.66739453488 units. h = ½(2√(2)-1...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2034047

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EG = 3AG Let AG = 1 unit. Therefore; EG = 3 units. The side length of the regular pentagon is; AG+EG = 1+3 = 4 units. AE = 4 units. It implies, Area Blue is; 0.5*2*4sin108 = 4sin108 = 3.80422606518 square units. Calculating Area Green. (DG)² = 3²+4²-2*3*4cos108 DG = 5.6935408899 units. It implies; 5.6935408899² = 2(GH)² (GH)² = 0.5(5.6935408899)² (GH)² = 16.20820393248 square units.  Area Green= ½(GH)² = 0.5*16.20820393248  = 8.10410196624 square units. Therefore; Area Blue ÷ Area G...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2033280

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Sir Mike Ambrose is the author of the question. Let the side of the blue square (length CD) be 1 unit. Area Blue is; 1² = 1 square unit. a = 180-20-40 a = 120° (b/sin40) = (1/sin20) b = 1.87938524157 units. (c/sin120) = (1/sin20) c = 2.53208888624 units. d² = 1²+1.87938524157²-2*1.87938524157cos60 d = 1.62871226577 units. Area Yellow is; (1.62871226577)² = 2.65270364467 square units. (a) Area Yellow ÷ Area Blue to 2 decimal places is; 2.65270364467 ÷ 1 = 2.65270364467 ≈ 2.65 (b) Calcul...
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