Mathematics Question and Solution

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

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

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

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

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

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

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.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2648447

Let a be the radius of the circle. It implies; a² = 16²+b²-2*16bcos45 a² = 256+b²-16√(2)b --- (1). a² = 8²+b²-2*8bcos135 a² = 64+b²+8√(2)b --- (2). Equating (1) and (2) to get b. 256+b²-16√(2)b = 64+b²+8√(2)b 192 = 24√(2)b 8 = √(2)b b = 4√(2) units. b = 5.6568542495 units. Calculating a, radius of the circle. Recall. a² = 256+b²-16√(2)b at (1). And b = 4√(2) units. a² = 256+(4√(2))²-16√(2)*4√(2) a² = 256+32-128 a² = 288-128 a² = 160 a = √(160) a = 4√(10) u...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2648428

a² = (8√(3))²+(3√(3))²-2*8√(3)*3√(3)cos60 a = 7√(3) units. a = 12.124355653 units. a is AC. (7√(3)/sin60) = (8√(3)/sinb) b = 81.7867892983° c = 180-b c = 98.2132107017° c is angle ACB. d = 2c d = 196.4264214035° e = 360-d e = 163.5735785965° e is angle AOB where O is the centre of the circle. f = ½(e) f = 81.7867892983° sin81.7867892983 = (0.5*8√(3))/g g = 7 units. g is the radius of the circle. Therefore, diameter of the circle is; Let it be h. h = 2g...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2648402

Let the single side length of the three side regular hexagon be 1 unit. Therefore; The width of the rectangle is; 2 units. The length/height of the rectangle is; 4 units. It implies; Area rectangle is; 4*2 = 8 square units. Calculating Area Purple. It is; Area rectangle with length 2 units and width 1.56698729811 units - Area triangle with height 1.56698729811 units and base (¼) units - Area triangle with height ¼(7) units and base 0.27919817891 units. = (...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2646699

Let the radius of the circle be a. b = (a-1) cm. c = (a-2) cm. It implies, observing Pythagoras rule to get a, radius of the circle. a² = b²+c² a² = (a-1)²+(a-2)² a² = a²-2a+1+a²-4a+4 0 = a²-6a²+5 Resolving the above quadratic equation via factorization approach to get a. It implies; a²-a-5a+5 = 0 a(a-1)-5(a-1) = 0 (a-1)(a-5) = 0 Therefore; a ≠ 1 cm. a = 5 cm. Recall. c = (a-2) And a = 5 cm. c = 5-2 c = 3 cm. Therefore; a² = c²+d² Where d is ha...

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