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Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2653410

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Let a be the radius of the half circle. (2a)² = 8²+3² 4a² = 73 a = ½√(73) units. b = 90-atan(3/8) b = atan(8/3)° Therefore, area blue triangle is; 0.5*½√(73)*(8+3)sin(atan(8/3)) = 0.25*11√(73)sin(atan(9/3) = 22 square units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2653238

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a = ½(180-45) a = 67.5° sin67.5 = (0.5*18)/b b = 9.7415298026 units. b is the radius of the half circle and the width of the rectangle. 2c² = b² 2c² = 9.7415298026² c = 6.8883017826 units. d = b+c d = 9.7415298026+6.8883017826 d = 16.6298315852 units. Therefore, area blue rectangle is; b*d = 9.7415298026*16.6298315852 = 162 square units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2651934

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a*6 = 12*8 a = 16 cm. a is DM. b² = 16²+12² b = 20 cm. b is BD. c = ½(16+6) c = 11 cm. d = ½(8+12) d = 10 cm. e = d-8 e = 2 cm. f² = 11²+2² f = 5√(5) cm. f is OD, radius of the circle. tang = 12/16 g = atan(3/4)° tanh = 2/11 h = atan(2/11)° j = g-h j = (atan(3/4)-atan(2/11)° j = 26.5650511771° Therefore, area red triangle is  0.5*5√(5)*20sin26.5650511771 = 50 cm²

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2651621

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2a² = 2² a² = 2 a = √(2) units. a is the radius of the inscribed blue quarter circle. Calculating R, radius of the inscribed circle. b = (√(2)+R) units. c = (√(2)-R) units. It implies; (√(2)+R)² = d²+(√(2)-R)² 2+2√(2)R+R² = d²+2-2√(2)R+R² d² = 4√(2)R d = √(4√(2)R) units. e = (2-R) units. Again, it implies; (2-R)² = R²+d² 4-4R+R² = R²+4√(2)R 4-4R = 4√(2)R 1-R = √(2)R (√(2)+1)R = 1 R = 1/(√(2)+1) R = (√(2)-1) units. R = 0.4142135624 units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2651553

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Observing the given yellow scalene triangle, an inscribed smaller scalene triangle that is similar the ascribed scalene triangle is identified. Please, move the above question left/right one time to review the both similar scalene triangles. Resolving the both triangles observing similar plane shape (scalene triangle) side length ratios. It implies; 6 - 4 4 - b Cross Multiply. 6b = 16 b = (8/3) units. c = 6-b c = (10/3) units. It implies; (10/3)² = (8/3)²+4²-2*4(8/...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2650290

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Calculating x, angle ABD a = ½(180-x)° a is angle BAD. It implies; x, angle ABD is, x+x+(a+39) = 180 (sum of the interior angles of the ascribed triangle) 2x+½(180-x) = 180-39 2x+½(180-x) = 141 4x+180-x = 282 3x = 282-180 3x = 102 x = 34°

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2649998

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Calculating R, radius adius of the circle. b = ½(6√(2)+8√(2)) b = 7√(2) units. c = b-6√(2) c = √(2) units. It implies; R² = c²+b² R² = √(2)²+(7√(2))² R² = 2+98 R = √(100) R = 10 units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2649974

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a² = 6²+(0.5*6)² a² = 36+9 a = √(45) a = 3√(5) units. Observing similar plane shape (right-angled) side length ratios. 3√(5) - (6+6) 3 - b Cross Multiply. 3√(5)b = 12*3 b = ⅕(12√(5)) units. b = 5.366563146 units. c²+b² = a² c²+(5.366563146)² = (3√(5))² c² = 45-28.8 c = √(16.2) c = 4.0249223595 units. Therefore, shaded blue area is; ¼(6²)π-(0.5*4.0249223595*5.366563146)-(0.5*6*3) = 9π-⅕(54)-9 = ⅕(45π-54-45) = ⅕(45π-99) square units  = 8.4743338823 square units....

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2649940

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a = 180-60 a = 120° b² = 2²+3²-2*2*3cos60 b² = 13-6 b = √(7) units. (√(7)/sin120) = (2/sinc) c = 40.8933946491° d = 60-c d = 19.1066053509° (√(7)/sin60) = (2/sine) e = 40.8933946491° f = 180-e f = 139.1066053509° g = 180-f-d g = 21.7867892982° It implies; (√(7)/sin21.7867892982) = ((2+h)/sin139.1066053509) √(3) = 0.742307489+hsin21.7867892982 h = (√(3)-0.742307489)/sin21.7867892982 h = 2.6666666666 h = ⅓(8) units. (√(7)/sin120) = (j/sin19.1066053509) j =...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2648497

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Let a be the radius of the circle and also, the width of the green rectangle. b = 180-45 b = 135° c = ½(45) c = 22.5° It implies; cos22.5 = d/10 d = 9.2387953251 units. d is the length of the green rectangle. Calculating a. cos22.5 = 5/a a = 5.4119610015 units. Therefore, area green rectangle is; a*d = 5.4119610015*9.2387953251 = 50 square units.
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