Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2054892

Let the blue diagonal be 1 unit. (1/sin110) = (a/sin30) a = 0.53208888624 units. (1/sin70) = (b/sin40) b = 0.68404028665 units. c² = 0.68404028665²+0.53208888624²-2*0.68404028665*0.53208888624cos110 c = 1 unit. (1/sin110) = (0.68404028665/sind) d = 40° Calculating the required angle, x. x+d+40 = 180 x+40+40 = 180 x = 180-80 x = 100°

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2054859

Sir Mike Ambrose is the author of the question. 12²=10²+10²-2*10*10cosa cosa = (200-144)/200 a = acos(56/200)° a = acos(7/25)° a = 73.73979529169° b = c = ½(180-73.73979529169) b = c = 53.13010235416° d² = 10²+10² d = 10√(2) cm e = ½d e = 5√(2) cm. Let PR = f. f² = 2(5√(2))²-2(5√(2))²cos(90+acos(7/25)) f = PR = 14 cm. g² = 6²+6² g = 6√(2) cm. Let PQ = h = QR h² = 50+72-2*60cos(90+53.13010235416) h = PQ = QR = 14.76482306023 cm. 14²=2(14.76482306023)²-2(14.76482306023)²cosi cosi = (2(1...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2054357

Sir Mike Ambrose is the author of the question. Let the radius of the ascribed quarter circle be 2 units. Area Quadrant is; ¼(4)π = π square units. The radius, r of the congruent inscribed semi-circles is; 2r+√(3)r = 2 r = 2/(2+√(3)) units. r = 0.53589838486 units. a = 2r a = 1.07179676972 units. b² = 1.07179676972²+0.53589838486²-0.53589838486*2*1.07179676972cos150 b = 1.55909609015 units. (1.55909609015/sin150) = (1.07179676972/sinc) c = 20.10390936081° d = 45-c d = 24.89609063919...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2052334

Sir Mike Ambrose is the author of the question. a = ½√(2²+2²) a = √(2) units. b² = (√(2))²+(√(2))² b = 2 units. c² = 3²+1² c = √(10) units. d = (135+atan(⅓))° e² = 10+2-2√(20)cos(135+atan(⅓)) e = 2√(5) units. (a) Calculating tan alpha exactly. Let alpha be x. (√(2)/sinx) = (2√(5)/sin(135+atan(⅓))) x = asin(√(2)/10) It implies; tanx is; tan(asin(√(2)/10)) = ⅐ (b) Calculating Green Area exactly. (f/sin(45+atan(⅓))) = (√(10)/sin(180-asin(⅒√(2))-(45+asin(⅓))) f = ⅓(4√(5)) units. g = (...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2050229

Sir Mike Ambrose is the author of the question. (a) Calculating Length Blue ÷ AB. Let AB be 1 unit. a² = 1²+1²-2cos108 a = 1.61803398875 units. b² = 1.61803398875²-0.5² b = 1.53884176859 units. c = 0.5+b c = 2.03884176859 units. cos54 = 0.5/d d = 0.85065080835 units. It implies; Length Blue (CD) is; (CD)² = 0.85065080835²+2.03884176859²-2*2.03884176859*0.85065080835cos108 CD = 2.43974693473 units. Therefore; Length Blue ÷ Length AB to 2 decimal places is; 2.43974693473 ÷ 1 = 2.43974...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2050221

Sir Mike Ambrose is the author of the question. Let the small regular hexagon be 2 units. a² = 2²+1²-2*2*1cos120 a = 2.64575131106 units. Where a is the side length of the big regular hexagon. (2.64575131106/sin120) = (1/sinb) b = 19.1066053509° c = 180-120-19.1066053509 c = 40.8933946491° (2.64575131106/sin40.8933946491) = (d/sin120) d = 3.5 units. Area Green is; Area triangle with height 2.64575131106 units and base 3.5sin19.1066053509 units. = 0.5*2.64575131106*3.5sin19.1066053509...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2049154

Let the big square side length be 1 unit. tan15 = a/1 a = 0.26794919243 units. b = 1-0.26794919243 b = 0.73205080757 units. sin75 = c/0.73205080757 c = 0.70710678119 units. c is the side length of the small square. cos75 = d/0.73205080757 d = 0.18946869098 units. cos15 = 1/e e = 1.03527618041 units. f = 1.03527618041+0.18946869098+0.70710678119 f = 1.93185165258 units. g² = 2*0.70710678119² g = 1 unit. h = 90+45+15 h = 150° j² = 2-2cos150 j = 1.93185165258 units. Calculating angle...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2047755

Let AB be 2 units. tan(atan½) = a/1 a = ½ unit. b = (atan(⅔))° tan(atan⅔) = c/1 c = ⅔ units. d = (180-atan⅔-atan2)° (e/sin(atan2)) = (1/sin (180-atan⅔-atan2)) e = ¼√(13) unit. It implies; Area Blue is; 2(area triangle with height ⅔ unit and base 1 unit - area triangle with height ¼√(13) unit and base sin(atan⅔) units. = 2(½*⅔*1- ½*¼*√(13)*sin(atan⅔)) = 2(⅓ - ¼) = 2(1/12) = ⅙ square units. Calculating Area Shaded. f² = (½)²+(⅓)² f = ⅙√(13) unit. g = f = ⅙√(13) unit. h² = 2(½)² h =...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2047743

Let the side length of the regular pentagon be 1 unit. a² = 2-2cos108 a = 1.61803398875 units. a is the side length of the square. sin18 = b/1 b = 0.30901699437 units. cos18 = c/1 c = 0.9510565163 units. d = 1.61803398875-0.9510565163 d = 0.66697747245 units. e = 1.61803398875-0.30901699437 e = 1.30901699438 units. It implies, the required angle x° is; tanx = 0.66697747245/1.30901699438 x = 27°

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2046199

Let AC be 2 units. a = √(2²+2²) a = √(8) units. a = 2√(2) units. Let the side length of the inscribed regular hexagon be b. c² = 2b²-2b²cos120 c = √(3)b units. d = 0.5b units. e = √(2) units. It implies; e+d+c = a √(2)+½(b)+√(3)b = 2√(2) ½(b)+√(3)b = √(2) b+2√(3)b = 2√(2) b = 2√(2)/(2√(3)+1) units. b = (4√(6)-2√(2))/11 units. Again, b is the side length of the inscribed regular hexagon. c = √(3)b c = √(3)(4√(6)-2√(2))/11 c = (12√(2)-2√(6))/11 units (((12√(2)-2√(6))/11)/sin90) = (f/sin...

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