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Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3649702

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Calculating green inscribed circle circumference.Let y be the radius of the green inscribed circle.Notice.ABCD is a square.Let x be the side length of the square which is also the radius of the inscribed quarter circle.a = ½(x) m.Calculating x.x² = (½x)²+6²x²-¼(x²) = 36¾x² = 363x² = 36*4x² = 48x = √(48)x = 4√(3) m.Again, x is the radius of the inscribed quarter circle and also the side length of the square.b = y+xb = (y+4√(3)) m.c = y-xc = (y-4√(3)) m.Calculating y.2c² = b²2(y-4√(3))² = (y+4√(3...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3648528

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Calculating x (AD).a = 6-5a = 1 unit.tanb = 3/1b = 71.5650511771°Notice.b is angle theta (angle ADC = angle BAD).c = (180-b)+(90-b)c = (180-71.5650511771)+(90-71.5650511771)c = 126.869897646°c is angle ABC.d² = 3²+5²-2*3*5cos126.869897646d = 7.21110255093 units.d is AC.(7.21110255093/sin126.869897646) = (5/sine)e = 33.6900675259°e is angle ACB.f = 90-ef = 90-33.6900675259f = 56.3099324741°f is angle ACD.It implies, length x is;(x/sin56.3099324741) = (7.21110255093/sin71.5650511771)x = 6.3245553...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3647293

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Calculating Area Inscribed SquareLet x be the length of the ascribed rectangle.a²+2² = x²a = √(x²-4) units.Calculating x.2 ~ √(x²-4)√(x²-4) ~ 1Cross Multiply.2 = x²-4x² = 6x = √(6) units.Again, x is the length of the ascribed rectangle.b²+x² = (1+2)²b²+√(6)² = 3²b² = 9-6b = √(3) units.b is the width of the ascribed rectangle.Let y be the side width of the inscribed rectangle .tanc = √(6)/√(3)c = atan(√(6)/√(3))°Calculating y.cosc = y/1cos(atan(√(6)/√(3))) = yy = 0.57735026919 units.y = ⅓√(3) un...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3646381

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Calculating the required red length.Let x be the side length of the ascribed square.a = ½(x) units.b = ⅓(x) units.tanc = (⅓(x))/xc = atan(⅓)°d = 180-45-cd = 135-atan(⅓)d = 116.565051177°Calculating x, side length of the ascribed square.(x/sin116.565051177) = (3/sin(atan(1/3)))x = 8.48528137424 units.tane = ½(x)/xe = atan(½)°f = 180-45-ef = 135-atan(½)°f = 108.434948823°Therefore, the required red length is;Let it be g.(8.48528137424/sin108.434948823) = (g/sin(atan(½))g = (8.48528137424sin(atan(...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3646366

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Calculating length H.Let r be the radius of the circle.a = 2r units.a is the diameter of the circle.b = 4+2+3b = 9 units.c = 2+3c = 5 units.d²+r² = 5²d = √(25-r²) units.e = r+de = (r+√(25-r²)) units.f = r-df = (r-√(25-r²)) units.Calculating r.4*5 = (r+√(25-r²))(r-√(25-r²))20 = r²-√(25-r²)²20 = r²-(25-r²)20+25 = 2r²r² = ½(45)r = √(½(45)) units.r = ½(3√(10)) units.Again, r is the radius of the circle.Recall.e = (r+√(25-r²)) units.And r = ½(3√(10)) units.It implies;e = ½(3√(10))+√(25-(½*3√(10))²)e...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3644741

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Calculating Area Blue.Let r be the radius of the biggest circle, also the side length of the blue square.a = 4+9a = 13 units.b = (r-4) units.c = (r-9) units.d = (r+9) units.e = (r-9) units.It implies;f²+(r-9)² = (r+9)²f² = r²+18r+81-(r²-18r+81)f² = 36rf = √(36r)f = 6√(r) units.g = 2r-4-9g = (2r-13) units.13² = (2r-13)²+ h²h² = 169-(4r²-52r+169)h² = 52r-4r²h = √(52r-4r²) units.j = (r+4) units.(r+4)² = (r-4)²+k²r²+8r+16 = r²-8r+16+k²k² = 16rk = √(16)rk = 4√(r) units.Calculating r.f = h+k6√(r) = √...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3644722

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Calculating Area Inscribed Blue Triangle (Equilateral Triangle).Let r be the radius of the inscribed six congruent circles.a+a+r+r = 52a = 5-2ra = ½(5-2r) units.b = ⅙*180(6-2)b = 120°c = ½(b)c = 60°Calculating r.tan60 = r/a√(3) = r/(½(5-2r))(5-2r)√(3) = 2r5√(3) = 2r+2√(3)r5√(3) = (2+2√(3))rr = (5√(3))/(2+2√(3))r = ¼(5(3-√(3)) units.r = 1.58493649054 units.Again, r is the radius of the inscribed six congruent circles.tan60 = d/(0.5*5)d = 0.5*5tan60d = 2.5√(3) units.d = 4.33012701892 units.d is h...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3643602

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Calculating angle x.Let BE be 1 unit.a = 180-55-20a = 105°a is angle CBE.b = a-30b = 105-30b = 75°b is angle ABE.(1/sin20) = (c/sin105)c = 2.82417818114 units.c is CE.d = 180-55-15-75d = 180-145d = 35°d is angle BAE.(1/sin35) = (e/sin75)e = 1.68404028665 units.e is AE.f² = c²+e²-2cecos15f² = 2.82417818114²+1.68404028665²-2*2.82417818114*1.68404028665cos15f = 1.27437435313 units.f is AC.It implies, angle x is;(1.27437435313/sin15) = (1.68404028665/sinx)sinx = 0.34202014332x = asin(0.34202014332)...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3643591

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Calculating area blue.tana = 24/32a = atan(3/4)°b² = 24²+32²b = √(24²+32²)b = 40 units.c = b-20c = 40-10c = 30 units.40 ~ 3024 ~ dCross Multiply.40d = 30*24d = ¼(3*24)d = 18 units.d is the top parallel length of area blue.f = 24-df = 24-18f = 6 units.g²+f² = 10²g² = 10²-6²g² = 100-36g = √(64)g = 8 units.g is the height of area blue.Therefore, blue area is;½(24+d)*g= ½(24+18)*8= ½*42*8= 21*8= 168 square units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3643586

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Calculating blue area.tana = 0.5(10)/10a = atan(½)°.b = 90-ab = atan(2)°.c = 180-45-ac = 135-atan(½)c = 108.434948823°It implies;(10/sin108.434948823) = (d/sin45)d = 7.453559925 cm.Therefore, area blue is;½*10*dsinb= 0.5*10*7.453559925sin(atan(2))= 33.3333333333 cm²= 33⅓ cm²
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