Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3067657

18² = 14²+16²-2*14*16cosa 448cosa = 14²+16²-18² a = acos((14²+16²-18²)/448) a = 73.39845040098° (18/sin73.39845040098) = (14/sinb) b = 48.18968510422° c = 180-48.18968510422-73.39845040098 c = 58.4118644948° cotd = cota+cotb+cotc cotd = 1.80748828181 d = acot(1.80748828181) d = 28.95373454979° e = 58.4118644948-d e = 29.45812994501° f = 180-28.95373454979-73.39845040098 f = 77.64781504923° (14/sin77.64781504923) = (g/sin73.39845040098) g = 13.73434221224 units....

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3066287

8 = 4 a = (8-a) Cross multiply. 64-8a = 4a 64 = 12a a = ⅓(16) cm. b = 8-a b = ⅓(8) cm. c = atan(⅔)° d = atan(3/2)° ⅔ = 8/e e = 12 cm ⅔ = f/8 f = ⅓(16) cm. g = 8-f g = ⅓(8) cm. Area Orange exactly in cm² is; Area square units side 8 cm - Area rectangle with length 4 cm and width ⅓(8) cm. = 8² - 4*⅓(8) = 64 - ⅓(32) = ⅓(192-32) = ⅓(160) cm²

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3064529

Area coloured regions is; Half the area of the ascribed square. = ½(2*2) = 2 square units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3063189

Sir Mike Ambrose is the author of the question. Let AC = 2 units. Therefore; AB = ⅖ unit. BC = (8/5) unit. It implies; Area Blue is; Area triangle with height ⅖ unit and base 2sin120 units + Area triangle with height 1 unit and base 0.4√(31)sin111.05172443535 units = (½*⅖*2sin120) + (½*1*0.4√(31)sin111.05172443535) = √(3)/5 + 1.03923048454 = 1.38564064606 square unit. Area Green is; Area triangle with height √(7) units and base 3√(21)/5 units = ½*√(7)...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3061909

Let AC be 1 unit. Area smaller pentagon is; ½(5)*(1/(2tan(36))) = 1.72047740059 square units. a² = 1²+0.5²-cos108 a = 1.24860602048 units. Where a is CD. (1.24860602048/sin108) = (0.5/sinb) b = 22.38617755917° c = 108-22.38617755917 c = 85.61382244083° Calculating Area E. It is; 0.5*0.5*0.5*1.24860602048sin22.38617755917 = 0.05944103227 square units. (a) Area E ÷ Area Smaller Pentagon to 3 decimal places is; 0.05944103227 ÷ 1.72047740059 = 0.034549...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3060364

Sir Mike Ambrose is the author of the question. Area R is; Area triangle with height 4 cm and base (4tan52.5) cm - Area sector with angle 52.5° and radius 4 cm. = ½*4(4tan52.5) - (52.5*4*4π)/360 = 8tan52.5 - ⅓(7π) = ⅓(24tan52.5-7π) = 3.09542012435 cm² ≈ 3.1 cm²

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3058839

a² = 10²+16²-2*10*16cos120 a = 2√(129) units. Where a is length AC. (3√(129)/sin120) = (16/sinb) b = 37.58908946897° c = 90-b c = 52.41091053103° d = 60-b d = 22.41091053103° e = 90-d e = 67.58908946897° f = 90-60 f = 30° cos37.58908946897 = g/10 g = 7.92405815693 units. i = 30+37.58908946897 i = 67.58908946897° tan67.58908946897 = j/7.92405815693 j = 19.2148198619 units. Where j is the radius of the arc. sin67.58908946897 = 19.2148198619/k k = 20....

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3057421

Let the radius of the inscribed half circle be 1 unit. Area rectangle is; 2*1 = 2 square units. Calculating Shaded Area as a single fraction.. It is; ½(1*2) - 1² + ¼(1)²π - ((180-2atan(½))π*1²/360) + (0.5*1²sin(180-2atan(½))) = 1-1+¼(π)-(π(180-2atan(½))/360)+⅖ = (π/4)+⅖-(π(180-2atan(½))/360) = ((5π+8)/20)-(π(180-2atan(½))/360) = (90π+144-180π+2πatan(½))/360 = (144-90π+2πatan(½))/360 square units. Therefore; Area Shaded ÷ Area Rectangle as a single fraction...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3055804

Let the two congruent lengths be 1 unit. tan40 = a/1 a = 0.83909963118 unit. cos40 = 1/b b = 1.30540728933 units. Calculating r, radius of the red inscribed circle. (r/tan(20)) + (r/tan(25)) = 1.30540728933 r = 0.26684617092 units. Red area is: π(0.26684617092)² = 0.22370300775 square units. Calculating Purple Area. cos40 = c/2 c = 1.53208888624 units. sin40 = 1/d d = 1.55572382686 Where c and d is the height and base of the rectangle respectively. t...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3054308

Let the radius of the semi circle be 1 unit. cos20 = a/2 a = 1.87938524157 units. cos20 = 1/b b = 1.06417777248 units. c = a-b c = 0.81520746909 unit. Where c is AB, the side of the square. Area Square is; (0.81520746909)² = 0.66456321766 square units. Calculating AF. sin20 = d/2 d = 0.68404028665 units. 0.68404028665 = e 1.87938524157 = 0.81520746909 cross multiply. 1.87938524157e = 0.81520746909*0.68404028665 e = 0.2967112535 unit. f² = 0.2967112535...

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