Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/1945925

Let the side of the regular pentagon be 1 unit. Notice; The regular pentagon side is equal the regular heptagon side. a = ⅐(180*5) a = ⅐(900)°, the single interior angle of the regular heptagon. b = 2a b = ⅐(450)° tan(⅐(450)) = c/0.5 c = 1.03826069829 units. cos(⅐(450)) = 0.5/d d = 1.15238243548 units. Where d is the radius of the ascribed circle. e = 180-⅐(900) e = ⅐(360)° tan18 = 0.5/f f = 1.53884176859 units. g² = 1.15238243548²-0.5² g = 1.03826069828 units. h = f-g h = 0.5005810...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/1945920

Let the side of the regular pentagon be 1 unit. a² = 2-2cos108 a = 1.61803398875 units. sin30 = b/0.5 b = 0.25 unit. c = 2b c = 0.5 unit. Where c is the inscribed square side. Area Square is; (0.5)² = 0.25 square units. Inscribed circle radius d is; d = ½(b) d = 0.125 unit. e = 0.5-0.125 e = 0.375 unit. f = 2atan(0.125/0.375) f = 36.86989764584° tan36.86989764584 = g/0.5 g = 0.375 unit. Shaded Area is; 0.5*0.375*0.5-π*0.125*0.125 = 0.04466261479 square units. (a) Area Shaded ÷...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/1945276

Let the radius of the circle be a. a² = 2²+4² a² = 20 a = 2√(5) cm. Area Blue is; Area half circle with radius 2√(5) cm - Area red rectangle with length and base 6 cm and 2 cm respectively. = ½(2√(5))²π - (6*2) = 10π-12 = 2(5π-6) cm² = 19.4159265359 cm²

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/1945219

Let the four congruent lengths be 1 unit each. a² = 2-2cos38 a = 0.65113630891 units. b = ½(180-38) b = 71° c = 60+71 c = 131° d² = 0.65113630891²+1²-2*0.65113630891cos131 d = 1.50941916044 units. Therefore; The required angle x is; (1/sinx) = (1.50941916044/sin131) x = 30°

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/1945064

Let a be the radius of the inscribed half circle. tanb = (3/4) b = atan(3/4)° tan(atan(3/4)) = a/(4-a) (3/4) = a/(4-a) 4a = 12-3a 7a = 12 a = (12/7) units. c² = 3²+4² c = √(25) c = 5 units. sin(atan(3/4)) = (12/7)/d (3/5) = (12/7)/d 3d = (60/7) d = (20/7) units. Calculating x. x = c-d-a x = 5-(20/7)-(12/7) x = 5-(32/7) x = ⅐(35-32) x = (3/7) unit.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/1944808

a = 360-140-80 a = 140° cos20 = 1/b b = 1.06417777248 units. (1.06417777248/sin30) = (c/sin70) c = 2 units. d² = 4+1.064177772482²-4*1.06417777248cos140 d = 2.89711998506 units. (2.89711998506/sin140) = (2/sine) e = 26.34291130662° f = 40-e f = 13.65708869338° g = 20+26.34291130662 g = 46.34291130662° tan46.34291130662 = h/2 h = 2.09602104183 units. Area ABC is; 0.5*2*2.09602104183 = 2.09602104183 square units. Calculating Area Blue. i = 60-26.34291130662 i = 33.65708869338= (1....

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/1944792

a² =2*12² a = 12√(2) cm. a = AC. 12b+12b+12√(2)b = 12*12 b = 144/(24+12√(2)) b = 12-6√(2) cm. b = 3.51471862576 cm. b = radius of the inscribed circle. BF = ½(12√(2)) BF = 6√(2) cm. c² = (6√(2))²+3.51471862576²-12√(2)*3.51471862576cos45 c = 6.49435320175 cm. c = EF. (6.49435320175/sin45) = (6√(2)/sind) d = 112.5° d = Angle BEF. e = 2(180-112.5-45) e = 45° f = 112.5-90 f = 22.5° cos22.5 = 12/g g = 12.98870640351 cm. g = EG. FG = 12.98870640351-6.49435320175 FG = 6.49435320176 cm. tan22...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/1944040

Let the side of the regular decagon which is equal the side of the regular octagon be 1 unit. Calculating Area Gold. a = ⅛(180*6) a = 135° b = ½(360-2(135)) b = 45° sin45 = c/1 c = ½(√(2)) units. d = 1+2c d = (1+√(2)) units. Area Gold is; Area regular octagon with side 1 unit - Area trapezoid with parallel sides 1 unit and (1+√(2)) units and height ½(√(2)) units. = ½(8*1)*(1/(2tan(180/8))-0.5(1+1+√(2))*(√(2)/2) = 4.82842712475-1.20710678119 = 3.62132034356 square units. Calculating...

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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/1943729

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...

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