Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2645013

Let the single side length of the hexagon be 2 units. Therefore; AG =√(8-8cos150) units. Calculating AH. AH = √((8-8cos150)+4-4√(8-8cos150)cos105) AH = 4.78834034195 units Therefore; MH = ½AH MH = 2.39417017098 units. Calculating MG. MG = √(2.39417017098²+2²-4(2.39417017098)cos51.2060231127) MG = 1.93185165257 units. Calculating angle MGH Let it be x. x = asin((2.39417017098sin51.2060231127)/1.93185165257) x = 75° Therefore; Angle FGM (angle alpha)...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2643746

a² = 2(15)² a = √(2(15)²) a = 15√(2) units. b²+21² = a² b² = 450-441 b² = 9 b = 3 units. tanc = 15/15 c = 45° tand = 3/21 d = atan(1/7)° e = 180-c-d e = 135-atan(1/7) e = (45+atan(7))° Therefore, Area Blue Inscribed Triangle is; 0.5*3*15sin(45+atan(7)) = ½*3*15*⅘ = 3*3*2 = 18 square units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2643538

cos30 = a/10 a = 5√(3) units. sin30 = b/10 b = 5 units. cos40 = c/10 c = 7.6604444312 units. sin40 = d/10 d = 6.4278760969 units. e = 180-30-40 e = 110° (10/sin110) = (f/sin30) f = 5.3208888624 units. g = 90-30 g = 60° h = 90-40 h = 50° j = 180-50-50 j = 80° k = 180-60-80 k = 40° (10/sin110) = (l/sin40) l = 6.8404028665 units. m = a-l m = 5√(3)-6.8404028665 m = 1.8198511713 units. n = c-f n = 7.6604444312-5.3208888624 n = 2.3395555688 units....

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2643485

Sir Mike Ambrose is the author of the question. Let the single side length of the inscribed regular hexagon be 2 units. Therefore; Area rectangle ABCD is: 2√(3) * 4 = 8√(3) square units. Area Blue will be; Area rectangle with length 4 units and width 2√(3) units - Area trapezium with two parallel length sum (1+4) units and height √(3) units - Area rectangle with length √(3) units and width 1 unit - Area triangle with height √(3)sin(atan√(3)) units and base √(3)cos(atan√(3)) u...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2643477

Let the radius of the inscribed red semi circle be r. Therefore; (8-r)²+(9-r)²=r² 64-16r+r²+81-18r+r²=r² r²-34r+145=0 (r-17)²=-145+(17)² r = 17±√(144) r = 17±12 It implies ; r ≠ 29 cm. r = 5 cm. Therefore area red inscribed semi circle is; ½π(5)² = ½(25π) cm² Area rectangle (green) is; 9 * 8 = 72 cm² It implies; Area red inscribed semi circle ÷ Area green rectangle is; ½(25π)÷72 = 25π/144 = 275/504

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2641858

Calculating r, radius of the circumcircle. 2(√(3)) + 2(√(3)) r = 4√(3) units. Therefore area of the circumcircle is; π(4√(3))² = 48π square units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2641852

Area blue is; Area triangle with height √(3) units and base 1 unit - Area sector with radius 1 unit and angle 60° - Area sector with radius 1 unit and angle 30° = ½√(3) - (π/6) - (π/12) = (6√(3)-2π-π))/12 = (6√(3)-3π)/12 = ¼(2√(3)-π) square units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2641845

Let the width of the square be x. Therefore the length of the square will be 2x. Calculating x. x² + x² = (2√(3²+3²)+2(3))² 2x² = (2√(18)+6)² 2x² = (6√(2)+6)² 2x² = 72+72√(2)+36 x² = 54+36√(2) x (rectangle width) = √(54+36√(2)) units. Therefore the length of the rectangle 2x is; = 2√(54+36√(2)) units. Therefore area of the rectangle is; 2√(54+36√(2)) * √(54+36√(2)) = 2(54+36√(2)) = 36(3+2√(2)) square units. = 209.823376491 square units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2641804

Sir Mike Ambrose is the author of the question. Let the single side length of triangle ABC be 2 units. Calculating Area ABC. ½(4sin60) = √(3) square units. Calculating Area Yellow. It is; Area equilateral triangle with side 2 units - Area triangle with two lengths 2 units and (√(2)/sin75) units, and angle 60°, the angle they form - Area triangle with two lengths 1 units and (1/sin105) units, and angle 15°, the angle they form. = √(3) - (√(6)/2sin75) - (sin15/(2sin105) =...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2640562

a = 180-60 a = 120° b = ½(8) b = 4 units. It implies; (8/sin120) = (4/sinc) c = 25.6589062733° d = 690-c d = 34.3410937267° Therefore, yellow area is; Area sector with radius 8 units and angle 34.3410937267° - Area triangle with height 8 units and base 4sin34.3410937267 units = (34.3410937267π*8*8÷360)-(0.5*8*4sin34.3410937267) = 19.1796849365-9.0258943816 = 10.1537905549 square units.

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