Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3215499

Calculating the required angle. Notice. The ascribed plane shape is a square, let it's side length be x. Let the longest side length of the inscribed red lengths triangle be 1 unit. a = 180-45-57 a = 180-102 a = 78° (1/sin78) = (b/sin45) b = 0.72290396731 units. (1/sin78) = (c/sin57) c = 0.85740696733 units. d²+x² = 0.85740696733² d = √(0.85740696733²-x²) units. cosy = x/0.85740696733 --- (1). siny = √(0.85740696733²-x²)/0.85740696733 --- (2). cos(45-y) = x/...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3214346

Notice. The ascribed quadrilateral is a square. Calculating x, the side length of the square. a²+x² = 8² a = √(64-x²) units. b²+x² = 10² b = √(100-x²) units. It implies;. c = (x-√(64-x²)) units. d = (x-√(100-x²)) units. Notice again. The inscribed triangle is a right-angle triangle. Therefore; √(x-√(100-x²) ~ √(64-x²) 6 ~ 8 Cross Multiply. 8(x-√(100-x²)) = 6√(64-x²) 4(x-√(100-x²)) = 3√(64-x²) 4x-4√(100-x²) = 3√(64-x²) 16x²-32x√(100-x²)+1600-16x² = 57...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3214296

Calculating Inscribed Blue Rectangle Area. a = 15+5 a = 20 units. a is the radius of the circle. Let b be the length of the blue inscribed rectangle. b² = 2(20)²-2(20)²cos(90-x) b² = 800-800(cos90cosx+sin90sinx) b² = 800-800sinx --- (1). Again. b² = 2(15)²-2(15)²cos(90+x) b² = 450-450(cos90cosx-sin90sinx) b² = 450-450(-sinx) b² = 450+450sinx --- (2). Calculating x. Therefore; Equating (1) and (2). 800-800sinx = 450+450sinx 350 = 1250sinx sinx = 7/25 x = asin...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3214260

Calculating Area Green. a = ⅙*180(6-2)-90 a = 120-90 a = 30° b = ½(a) b = 15° c = 180-15-120 c = 45° It implies; (d/sin45) = (1/sin15) d = (1+√(3)) units. d = 2.73205080757 units. d is the side length of the regular hexagon. e = d-1 e = 1+√(3)-1 e = √(3) units. e is the side length of the green area (square). Green square area is; e² = √(3)² = 3 square units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3214253

Calculating x, side length of the largest ascribed square. a =14+9 a = 23 units. b² = 23²+7² b = √(578) b = 17√(2) units. b is the diagonal of the largest square. It implies, x is; 2x² = b² 2x² = (17√(2))² 2x²= 2(17)² x² = 17² x = 17 units. Again, x is the side length of the largest square.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3214247

Kindly move the question right/left one time to review the framework/analysis. Thank you nicely. Calculating Area Inscribed Blue Rectangle. a = 15+5 a = 20 units. a is the radius of the circle. d² = b²+c² --- (1). Where b is the width of the inscribed blue rectangle area and c is the length. 15²+20² = d² d = 25 units. d is the diagonal of the inscribed blue rectangle. Substituting d is (1) making c the subject formula. d² = b²+c² 25² = b²+c² c = √(625-b²) units. Again,...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3213003

Calculating Shaded Blue Area. Notice. ½(10) = 5 cm is the radius of the inscribed circle. a² = 2(10)² a = 10√(2) cm. a is the diagonal of the ascribed square. b = ½(a) b = 5√(2) cm. It implies; 10² = 5²+(5√(2))²-2*5*5√(2)cosc 100 = 25+50-50√(2)cosc 50√(2)cosc = 75-100 cosc = -(25)/(50√(2)) c = acos(-¼*√(2)) c = 110.704811055° d = 2c d = 221.409622109° e = 360-d e = 138.590377891° (5/sinf) = (10/sin110.704811055) f = 27.8855668363° g = 2f g = 55.771133...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3212999

Calculating fraction of yellow shaded area. Let the single side length of the square be 2 units. Area yellow (shaded area) is; ½(4) square units. = 2 square units. Area square is; 2x2 = 4 square units. Therefore fraction of shaded area is; Area yellow ÷ Area square = 2÷4 = ½

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3211958

Kindly move the question right/left one time to review the framework/analysis of the question. Thank you nicely. Calculating length DG. Let x be the side length of the square. Let h be the height of triangle ADG. Let a be the height of triangle CDG. It implies; ½(xh ) = 18 xh = 36 cm² Observing Similar Plane Shape Rule. Consider triangle CDG and height a. h ~ a a ~ (x-h) Cross Multiply. a² = xh-h² And xh = 36 cm² a² = 36-h² a²+h² = 36 Length DG...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3211729

Calculating Shaded Area. Let the radius of the semi circle be r. Calculating r. 2+√(5/2)r ~ ½(3r) 2r ~ √(5/2)r Cross multiply. 3r² = 2√(5/2)r + (5/2)r² (½)r² = 2√(5/2)r (¼)r² = √(5/2)r (1/16)r⁴ = (5/2)r² (r²/16) = (5/2) 2r² = 80 r² = 40 r = √(40) r = 2√(10) units. Therefore radius, q of the inscribed circle is; q = ½(r) q = ½(2√(10)) q = √(10) units. It implies shaded area will be; Area ascribed semi circle with radius...

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Mathematics Question and Solution

Mathematics Question and Solution

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Mathematics Question and Solution

Mathematics Question and Solution

Mathematics Question and Solution

Mathematics Question and Solution

Mathematics Question and Solution

Mathematics Question and Solution

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