Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2468245

Sir Mike Ambrose is the author of the question. Let the side length of the regular ascribed pentagon be 1 unit. a = ⅕*180(5-2) a = 108° a is the single interior angle of the regular pentagon. Let the inscribed square side length be b. (b/sin108) = (c/sin18) c = 0.3249196962b units. sin54 = (0.5b/d) d = 0.6180339887b It implies, b is; c+d = 1 0.3249196962b+0.6180339887b = 1 0.9429536849b = 1 b = 1.060497473 units. Again, b is the side length of the inscribed square....

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2467648

a = ½(10) a = 5 cm. a is the radius of the ascribed semi circle. b = (5-c) cm. c is the radius of the inscribed blue circle. It implies; (5-c)² = c²+d² 25-10c+c² = c²+d² d² = 25-10c d = √(25-10c) cm. e = 5+d e = (5+√(25-10c)) cm. Therefore; calculation c, radius of the blue inscribed circle. tan15 = c/(5+√(25-10c)) 0.2679491924(5+√CT(25-10c)) = c c-1.3397459622 = 0.2679491924√(25-10c) (3.732050808c-5)² = 25-10c 13.9282032335c²-37.32050808c+25 = 25-10c 13.9282032335c² = 27.32050808c 13.9...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2466950

Notice! A regular triangle (equilateral triangle) with side length 2 units is inscribed the quarter circle due to the apex vertices of the two equilateral triangles on point the circumference of the quarter circle. Therefore, radius of the quarter circle is 2 units. It implies; Area quarter circle is; ¼(2²)π = π square units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2466887

Area R is; Area sector with radius 8 cm and angle 20.16632290743° - Area triangle with height 8 cm and base (4.2sin 20.16632290743) cm = ( 20.16632290743 *64π÷360) - (½*8*4.2sin 20.16632290743) = 11.26299944816 - 5.79174146157 = 5.47125798659 cm² ≈ 5.47 cm²

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2466792

Let BC = 1 unit. (1/sin36) = (a/sin72) a = 1.6180339887 units. a is BD = CD. b = 180-12-30 b = 138° b is angle BAD. (1.6180339887/sin138) = (c/sin30) c = 1.2090569265 units. c is AB. d² = 1.2090569265²+1-2*1.2090569265cos84 d = 1.4862896509 units. d is AC. (1/sine) = (1.4862896509/sin84) e = 42° e is angle BAC. f = b-e f = 138-42 f = 96° f is angle CAD. Therefore, the required angle, angle ACD (x) is; x = 180-30-36-f x = 180-66-96 x = 180-162 x = 18°

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2466318

Area coloured is; Area sector with radius 3 units and angle 120° - Area triangle with height 3 units and base 3sin120 units + Area triangle with height 3 units and base 3sin60 = (120*9π÷360) - (½*9*½*√(3)) + (½*9*½√(3)) = 3π - ¼(9√(3)) + ¼(9√(3)) = 3π square units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2465151

Let the congruent two inscribed semi circles radius be r. a = (3-2r) units. b = 2r units. It implies, calculating r. 2²+a² = b² 2²+(3-2r)² = (2r)² 4+9-12r+4r² = 4r² 12r = 13 r = (13/12) units. Again, r is the radius of the inscribed two congruent semi circles. Are Blue is; Area rectangle with length 3 units and width 2 units - Area circle with radius (13/12) units. = (3*2)-π(13/12)² = 6-(169/144)π = (864-169π)/144 square units. = 2.3129919552 square units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2463816

a = 36+18 a = 54° Let one of the green triangle area side be b. cos54 = c/b c = bcos54 units. c = 0.5877852523b units. sin54 = d/b d = bsin54 units. d = 0.8090169944b units. e = c+d e = 0.5877852523b+0.8090169944b e = 1.3968022467b units. Calculating b. 0.5*1.3968022467b*bsin54 = 22 1.3968022467b² = 44 b² = 31.500522071 b = 5.6125325897 units. e = 1.3968022467b units. And b = 5.6125325897 units. e = 1.3968022467*5.6125325897 e = 7.839598131 units. f² = 7.8...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2463796

sin36 = c/b c = bsin36 units. c = 0.5877852523b units. Calculating b. b² = (0.5877852523b)²+(0.5(b+1))² 0.6545084972b² = ¼(b²+2b+1) 1.6180339888b²-2b-1 = 0 It implies; b = 1.61803 units. Therefore; a = b+1 And b = 1.61803 units. a = 1.61803+1 a = 2.61803 units. cos72 = d/1.61803 d = 0.4999987674 units. sin72 = e/1.61803 e = 1.5388379751 units. f = 2.61803+1.5388379751 f = 4.1568679751 units. g = 1.61803+0.4999987674 g = 2.1180287674 units. tanh = 4.156...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2463750

Let the side length of the regular hexagon be 1 unit. a² = 2-2cos120 a = √(3) units. Area regular hexagon is; 2(½*sin120)+(1*√(3)) = ½√(3)+√(3) = ½(3√(3)) square units. = 2.5980762114 square units. Calculating yellow area. b² = 2(0.5)²-2(0.5)²cos120 b = ½√(3) units. c = ½(a-b) c = ½(√(3)-½√(3)) c = ¼√(3) units. cos60 = d/0.5 d = ¼ units. e = c-d e = ¼√(3)-¼ e = ¼(√(3)-1) units. Area yellow is; Area regular hexagon with side length 1 unit - Area triangle...

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