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Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2398248

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tana = 3/4 a = atan(3/4)° b = atan(4/3)° sin(atan(3/4)) = c/4 c = 2.4 units. Area Blue is; Area semi circle with radius 2.5 units - Area sector with radius 2 units and angle (180-2atan(3/4))° + 2(Area triangle with height 2 units and base 2sin(180-2atan(3/4)) units) - Area sector with radius 1.5 units and angle (180-2atan(4/3))° + 2(Area triangle with height 1.5 units and base 1.5sin(180-2atan(4/3)) units) + 2(Area triangle with height 2 units and base 2sin(2atan(3/4)) units) + 2(Area tria...

We are smart and clever!

https://onlineedumath.com/update/we-are-smart-and-clever/2398027

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Online Edumath Educators and Learners are Super Smart and Amazingly, Very Clever. Communicate us to mentor/teach/educate your child/children Mathematics online at affordable tuition, helping them become a lover of Mathematics, and also, a Mathematician. Call/WhatsApp: +2349076614992 or +2348152827445 Email: [email protected] [email protected] [email protected] Facebook Page: Online Edumath We are super smart and amazingly, very clever!

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2397914

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tan30 = 4/a a = 4√(3) units. sin30 = 4/b b = 8 units. c = b-2 c = 8-2 c = 6 units. Therefore, Area Blue is; Area semi circle with radius 4 units - Area sector with radius 2√(3) units and angle 120° + Area triangle with height 2√(3) units and base 2√(3)sin120 units - Area sector with radius 2 units and angle 60° + Area triangle with height 2 units and base 2sin60 units + Area sector with radius 2 units and angle 120° - Area triangle with height 2 units and base 2sin120 units + Ar...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2397773

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Calculating x (length BE). sin60 = a/8 a = 4√(3) units. a is DE. cos60 = b/8 b = 4 units. b is AD c² = 2²+(2√(3))² c = √(4+12) c = 4 units. d = (4+x) units. Therefore, length x (BE) is; Observing  Sine Rule. (4+x)/sin60 = 10/sin60 (4+x) = 10 x = 10-4 x = 6 units

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2397700

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a² = 6²+8²-2*6*8cos30 a = 4.10628314132 cm. a = DE. (4.10628314132/sin30) = (8/sinb) b = 103.06431342951° b = Angle ADE. Angle AED = 180-30-103.06431342951  = 46.93568657049° tan30 = c/6 c = 3.46410161514 cm. c = CH. d = 8-2*3.46410161514  d = 1.07179676972 cm. e = 1.07179676972+3.46410161514 e = 4.53589838486 cm. f = atan(6/4.53589838486)  f = 52.91133691903° g = 90-52.91133691903  g = 37.08866308097° h = 37.08866308097-30 h = 7.08866308097° i = 60+46.93568657049 i = 106.93568657049°...

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/2397140

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a = ½(4+6) a = 5 cm. a is the radius of the ascribed semi circle. Let b be the radius of the blue inscribed semi circle. c = 5-4 c =  1 cm. It implies; b²+c² = d² d² = b²+1² d = √(b²+1) cm. Therefore, calculate b, radius of the blue inscribed semi circle. 5² = d²+b² 25 = √(b²+1)²+b² 25 = 2b²+1 2b² = 24 b = √(12) b = 2√(3) cm. It implies, area blue is; ½(b)²π = ½(2√(3))²π = 6π square cm² = 18.8495559215 cm²

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2396754

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a² = 12²-6² a = 6√(3) cm. a = 10.39230484541 cm. a = circle's radius = AD = AG. b² = 2*10.39230484541²-2*10.39230484541²cos120 b = 18 cm. b = DG. c = 12-10.39230484541 c = 1.60769515459 cm. c = CD. d² = 12²+1.60769515459²-24*1.60769515459cos60 d = 11.28239078631 cm. d = BD. (11.28239078631/sin60) = (1.60769515459/sine) e = 7.088663081° e = Angle CBD. f = 60-7.088663081 f = 52.911336919° f = Angle DBG. (12/sing) = (10.39230484541/sin52.911336919) g = 112.91133691899° g = Angle BEG. Angle...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2396572

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Calculating r, radius of the circle. a*5 = 3*6 a = 18/5 a = 3.6 units. a is Length BP. b = ½(5+3.6) b = 4.3 units c = ½(3+6) c = 4.5 units. d = 4.5-3 d = 1.5 units. It implies; r² = b²+d² r² = 4.3²+1.5² r = √(4.3²+1.5²) r = √(20.74) r = 4.5541190147 units. r = 4.55 units to 2 decimal places. Again, r is the radius of the circle.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2396165

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Let r be the radius of the inscribed circle. a = (2-r) units. (2-r)² = r²+b² b² = 4-4r+r²-r² b = √(4-4r) units. c = (1+r) units. d = (1+√(4-4r)) units. It implies, observing Pythagoras Rule on a right-angled triangle with adjacent sides r units and (1+√(4-4r)) units, and hypotenuse (1+r) units to get r, radius of the inscribed circle. (1+r)² = r²+(1+√(4-4r))² 1+2r+r² = r²+1+2√(4-4r)+4-4r 6r-4 = 2√(4-4r) 3r-2 = √(4-4r) (3r-2)² = 4-4r 9r²-12r+4 = 4-4r 9r² = 8r 9r = 8 r = (8/9) units. Agai...
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