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Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2585177

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Let a be 1 unit. b = 1+(2*1)+1 b = 4 units. c = ½(b) c = 2 units. 2d² = 4² d² = 8 d = 2√(2) units. e² = 1²+(2√(2))²-2*2√(2)cos45 e = √(9-4) e = √(5) units. (√(5)/sin45) = (1/sinf) f = 18.4349488229° g = 90-2f g = 53.1301023542° h = ½(g) h = 26.5650511771° J² = 2k² j = √(2)k units. k is the radius of the circle. l = (2-√(2)k) units. k² = 1²+(2-√(2)k)² k² = 1+4-4√(2)k+2k² k²-4√(2)k+5 = 0 Calculating k via completing the square approach. (k-2√(2)...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2530541

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Notice! The ascribed polygon is a regular dodecagon (12 sides and 12 interior angles equal). It's since interior angle is; a = 180(12-2)/12 a = 1800/12 a = 150° The middle inscribed polygon is a regular octagon (8 sides and 8 interior angles equal). It's since interior angle is; b = ⅛*180(8-2) b = ⅛*(1080) b = 135° The completely inscribed polygon is a regular hexagon (6 sides and 6 interior angles equal). It's since interior angle is; c = ⅙*180(6-2) c = ⅙*(720) c = 120°...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2512953

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a = ⅐*180(7-2) a = ⅐(900)° a is the single interior angle of the regular heptagon. (√(2)/sin(900/7)) = (1/sinb) b = 33.5619539118° c = 180-(900/7)-b c = 17.8666175168° (d/sin17.8666175168) = (√(2)/sin(900/7)) d = 0.5549581321 units. e = 1-d e = 0.4450418679 units. f² = 2-2cos(900/7) f = 1.8019377358 units. g = ½(180-(900/7)) g = 25.7142857143° h = (900/7)-g h = 102.8571428571° Therefore, length AB is; Let it be j. j² = 1.8019377358²+0.4450418679²-2*1.80193...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2487952

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Let the three equal lengths of the ascribed pentagon be 1 unit each. a² = 2-2cos80 a = 1.2855752194 units. b = ½(180-80) b = 50° c = 80-b c = 30° d = 90-b d = 40° It implies; (1.2855752194/sine) = (1/sin30) e = 40° 30+40+40+f = 180 f = 180-110 f = 70° g = 180-70-80 g = 30° (1/sin30) = (h/sin70) h = 1.8793852416 units. j² = 1+1.2855752194²-2*1.2855752194cos(70+40) j = 1.8793852416 units. Notice; h = j It implies; k = ½(180-(80-40)) k = ½(180...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2473184

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15² = a²+6² a² = 225-36 a = √(189) a = 3√(21) units. b = 2a b = 6√(21) units. sin75 = c/b c = 6√(21)sin74 c = 26.5585692881 units  d = 10+c d = 36.5585692881 units. cos75 = e/(6√(21)) e = 7.1163471929 units. sinf = 6/15 f = 23.5781784782° g = 75-f g = 51.4218215218° h = 180-2g h = 77.1563569564° j² = 2*15²-2*15²cos77.1563569564 j = 18.7074571083 units. k = 15-½(j) k = 5.6462714458 units. l = k+5+j-e l = 22.2373813613 units. m = j-e m = 18.7074571...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2397396

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Notice, radius of the three congruent circles is 7 cm each. sin60 = a/14 a = 7√(3) cm. a = 12.124355653 cm. b = a+7+7 b = (7√(3)+14) cm. b = 26.124355653 cm. b is the length of the rectangle. tan30 = c/7 c = ⅓(7√(3)) cm. c = 4.0414518843 cm. d = 7+7+2c d = (14+⅓(14√(3)) cm. d = 22.0829037687 cm. d is the width of the rectangle. tane = ⅓(7√(3))/7 e = atan(⅓√(3))° e = 30° cosf = ⅓(7√(3))/7 f = acos(⅓√(3))° f = 54.7356103172° g = 90-e g = 90-atan(⅓√(3)) g = atan(√(3)) g = 60° h = 180-60-5...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2384366

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Let the side of the ascribed regular hexagon be 1 unit. a = ⅙(180(6-2)) a = 120° a is the single interior angle of the ascribed regular hexagon. b² = 1²+1²-2*1*1cos120 b = √(3) units. b is the height of the ascribed regular hexagon. c = ½(b) c = ½(√(3)) units. cos60 = d/1 d = ½ units. e = 2d+1 e = 2*½+1 e = 2 units.   It implies, area ascribed regular hexagon is; 2(½(1+2)*½(√(3))) = 2(½*3*½*√(3)) = ½(3√(3)) square units. = 2.5980762114 square units. Calculating area inscribed red regul...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2377561

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Let the radius of the small yellow inscribed circle be a. Let the radius of the big green inscribed circle be b. Notice! PQ = a+b Calculating radius of the ascribed semi circle. c² = 12²+16² c = √(144+256) c = √(400) c = 20 units. c is the diameter of the ascribed semi circle. d = ½(c) d = ½(20) d = 10 units. d is the radius of the ascribed semi circle. tane = 16/12 e = atan(4/3)° e is angle BAC. sin(atan(4/3)) = f/12 4/5 =f/12 f =48/5 f = 9.6 units. cos(atan(4/3)) = g/12 3/5 = g/12 g =...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2370714

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1. The proof that triangle EGH is equilateral. Let the side length of the regular hexagon be 1 unit. a = ⅙(180(6-2)) a = 30*4 a = 120° a is single interior angle of the regular hexagon. b² = 1²+0.5²-2*0.5cos120 b = 1.3228756555 units. b is EG. (1.3228756555/sin120) = (0.5/sinc) c = 19.1066053509° c is angle DEG. d² = 2-2cos120 d = 1.7320508076 units. d is BF. e = ½(d) e = ½(1.7320508076) e = 0.8660254038 units. e is FH. g² = 1²+0.8660254038² g = 1.3228756555 units. g is EH. Notice! EH...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2370478

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Let the side length of the regular octagon be 1 unit. a = ⅛(180(8-2)) a = ⅛(180*6) a = 3*45 a = 135° a is the single interior angle of the regular octagon. b = ½(360-135-135) b = ½(360-270) b = ½(90) b = 45° c = ½(180-135) c = ½(45) c = 22.5° d = 135-45-22.5 d = 90-22.5 d = 67.5° e = (180(5-2)) e = (180*3) e = 540° e is the sum of interior angles of a regular pentagon. f = ½(540-3(135)) f = ½(540-405) f = ½(135) f = 67.5° g = f-c g = 67.5-22.5 g = 45° h = 180-d-g h = 180-67.5-45 h = 13...
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