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Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/1956663

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Notice; ½(R) units is the radius of the inscribed half circle. Therefore; The length of the ascribed square is; 2*½(R) = R units. tana = (R/(0.5R) a = atan(2)° b = (180-2ata(2))° Calculating r, radius of the inscribed circle. Considering sine rule. ((0.5R+r)/sin(atan2)) = (0.5R/sin(180-2atan2)) ((0.5R+r)/(2√(5)/5)) = (0.5R/(4/5)) ⅕(4*(½(R)+r)) = ½(R)*⅕*2√(5) ⅕(2R+4r) = ⅕*√(5)R 2R+4r = √(5)R 4r = (√(5)-2)R r = ¼(√(5)-2)R units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/1956545

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Let the square side be 2 units. Calculating the radius of the yellow circle inscribed triangle BGE. Let it be x. (0.5)²+1 = a² a = ½√(5) units. a is EG = BG. x+2(½√(5))x = 1 (1+√(5))x = 1 x = 1/(1+√(5)) units. Calculating the radius of the yellow circle inscribed triangle CGF. Let it be y. b² = 1+2² b = √(5) units. b is CF. CG = ½(b) CG = ½√(5) units. FG = 1+½ FG = (3/2) units. FG = 1.5 units. Therefore; √(5)y+½√(5)y+½(3y) = (2-½) √(5)y+½√(5)y+½(3y) = (3/2) 2√(5)y+√(5)y+3y = 3 3√(5)...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/1956220

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a = atan(6/12) a = 26.56505117708° a = Angle BAE. b = 45-26.56505117708 b = 18.43494882292° b = Angle CAE. d = ½√(2*12²) d = 6√(2) cm. d = half AC = radius of the circle. Let the centre of the circle be O. e = 180-2(18.43494882292) e = 143.13010235416° e = Angle AOF. f² = 2*(6√(2))²-2*(6√(2))²cos143.13010235416 f = 16.099689438 cm. f = AF. g = 90-18.43494882292 g = 71.56505117708° g = Angle AFN. h = 180-71.56505117708-26.56505117708 h = 81.86989764584° h = Angle ANF. (16.099689438/sin8...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/1955187

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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 = 0.2967112535²+0.81520746909² f = 0.8675256...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/1954045

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Let the square side be 2 units. Notice; a+b = c --- (1). 2√(2) = c+a 2√(2)-a = c --- (2). a² = 2d² d = (a/√(2)) units. e = 2-d e = (2-(a/√(2))) units. b² = (2-(a/√(2)))²+(a/√(2))² b² = 4-(4a/√(2))+½(a²)+½(a²) b = √(4-(4a/√(2))+a²) --- (3). At (1). a+b = c Substituting (3) in (1). a+√(4-(4a/√(2))+a²) = c --- (4). Substituting (2) in (4). a+√(4-(4a/√(2))+a²) = 2√(2)-a √(4-(4a/√(2))+a²) = 2√(2)-2a 4-(4a/√(2))+a² = 8-8√(2)a+4a² 3a²-8√(2)a+2√(2)a+4 = 0 3a²-6√(2)a+4 = 0 3a²-8.48528137424a+4...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/1952625

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Let the square side, x be 1 unit. sin67.5 = a/1 a = 0.92387953251 units. cos67.5 = b/1 b = 0.38268343237 units. c = 2b c = 0.76536686473 units. d² = 1²+1² d = √(2) units. sin67.5 = e/√(2) e = 1.30656296488 units. e is the radius of the half circle. f = e-c f = 1.30656296488-0.76536686473 f = 0.54119610015 units. g = r-b g = (r-0.38268343237) units. r² = (r-0.38268343237)²+h² h² = r²-r²+0.76536686474r-0.14644660941 h² = 0.76536686474r-0.14644660941 h = √(0...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/1952379

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Let the side of the regular pentagon be 1 unit. Calculating Area Red. a² = 1²+1²-2*1*1cos108 a = 1.61803398875 units. b = 108-36-60 b = 12° (c/sin12) = (1.61803398875/sin96) c = 0.33826121272 unit. d = 1-c d = 0.66173878728 unit. e = 96-60 e = 36° tan36 = f/0.66173878728 f = 0.48078137139 unit. Area Red is; ½(df) = 0.5*0.48078137139*0.66173878728 = 0.15907584083 square units. Calculating Area Lilac. sin36 = 0.48078137139/g g = 0.81795412443 units. h = 1-f h = 0.51921862861 unit....

We are smart and clever!

https://onlineedumath.com/update/we-are-smart-and-clever/1952015

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Our certified, experienced, resilient, productive and committed Math Educators will be glad to be at your service. We make teaching and learning Mathematics fun for learners, we expose the simplicity and beauty of Mathematics to our learners, and mentor them to appreciate and love Mathematics. Communicate us to mentor/educate you Mathematics better online at affordable tuition. We are smart and clever.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/1952000

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a² = 15²+12²-2*12*15cos120 a = 23.43074902772 cm. Where a is the side length of the equilateral triangle ABC. (23.43074902772/sin120) = (12/sinb) b = 26.32950349168° c = 60-b c = 33.67049650832° d² = 15²+15²-2*15*15cos120 d = 25.98076211353 cm. e = atan(7.5/25.98076211353) e = 16.10211375199° f = 90-e f = 73.89788624801° g = 180-f-c g = 72.43161724367° (15/sin72.43161724367) = (h/sin73.89788624801) h = 15.11661227595 cm. i = a-h  i = 8.31413675177 cm. Let the radius of the green ins...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/1951105

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Let the side length of triangle ABC be 1 unit. a = 120-78 a = 42° b = 60-42 b = 18° (1/sin42) = (c/sin18) c = 0.4618186516 unit. tan60 = d/0.5 d = 0.86602540378 unit. Area Green is; 0.5*0.4618186516*0.86602540378 = 0.19997334211 square units. e = ⅓ unit. Where e is the side length of the red inscribed regular hexagon. Area Red is; ½*6*(⅓)²*(1/2tan(30)) = ⅓*(1/2tan(30)) = 0.28867513459 square units. f = 60+b f = 78° g = 180-2(78) g = 24° h = 1+c h = 1.4618186516 units. Where h i...
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