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Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3495549

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Calculating R, radius of the circle.Let alpha be x.a² = 11²+37²-2*11*37cosxa² = 1490-814cosx --- (1).a² = 37²+26²-2*26*37cosxa² = 2045-1924cosx --- (2).Equating (1) and (2) to get alpha (x)1490-814cosx = 2045-1924cosx1924cosx-814cosx = 2045-14901110cosx = 555cosx = 555/1110x (alpha) = 60°It implies, calculating a using (1).a² = 1490-814cos60a = 32.9089653438 units.b = ½(a)b = 16.4544826719 units.Therefore, R, radius of the circle is;sin60 = 16.4544826719/RR = 16.4544826719/sin60R = 19 units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3494821

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Calculating R, radius of the circle.a = 30+45a = 75°b = 180-75-60b = 45°8² = 2c²c² = 32c = 4√(2) units.sin30 = 4√(2)/dd = 8√(2) units.e = 2*45°e = 90°Therefore, R, radius of the circle is;2R² = (8√(2))²2R² = 128R² = 64R = 8 units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3493886

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Calculating Area Yellow.a = ½(180-30)a = 75°2² = b²+1²b² = 4-1b = √(3) units.Yellow Area is;2(Area triangle with height √(3) units and base 1 unit + 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 30° + Area triangle with height 2 units and base 2sin30 units - Area sector with radius 1 unit and angle 75°)= 2((½*√(3)*1)+(60π*2²/360)-(½*2*2sin60)-(30π*2²/360)+(½*2*2sin30)-(75π/360))= 2((0.5√(3))+(⅔...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3493151

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Sir Mike Ambrose is the author of the question.Let the single side length of the square be 2 units.Therefore;Area square is;2²= 4 square unitsIt implies;Area R is;Area sector with radius 2 units and angle 8.130127545 - Area triangle with height 1.61624318301 unit and base (1.37930921037sin8.130127545) units.= (8.130127545*4π÷360) - (½*1.61624318301*1.37930921037sin8.130127545)= 0.28379498853 - 0.15763573684= 0.12615925169 square units.Therefore;Area Square ÷ Area R to 1 d. p. is4 ÷ 0.126159251...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3492017

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Calculating Length CD.a = 15-11.25 a = 3.75 m.b = atan(3/3.75)°c = 90-atan(3/3.75)c = 51.34019174591° Therefore, Length CD is;tan(51.34019174591) = 15/CDCD = 15/tan(51.34019174591) CD = 12 m.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3491280

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Calculating Blue Area.Area blue is;Area sector with radius 10 cm and angle 2atan(½) - Area triangle with height 10 cm and base 10sin(2atan(½)) cm + Area sector with radius 5 cm and angle 2atan(2) - Area triangle with height 5 cm and base 5sin(2atan(2)) cm - 2(area quarter circle with radius 5 cm - area triangle with height 5 cm and base 5 cm).= (2atan(½)*100π÷360) - (½*100sin(2atan(½))) + (2atan(2)*25π÷360) - (½*25sin(2atan(2))) - 2((¼*25π)-(½*25))= 46.3647609001 - 40 + 27.6787179449 - 10 - 2(1...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3490651

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Sir Mike Ambrose is the author of the question.Inscribed square single side length is;7.80540954246 cmArea green in cm² to 1 decimal place is;Area trapezoid with parallel sides 12 cm and 7.25948291225 cm, and height 12 cm - Area square with side 7.80540954246 cm - Area triangle with height 7.25948291225 cm and base 2.86780856615 cm.= ½*12(12+7.25948291225) - 7.80540954246² - ½*7.25948291225*2.86780856615= 115.556897474 - 60.9244181255 - 10.4094036408= 44.2230757077 cm²≈ 44.2 cm²

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3489793

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Area green is;½*6*8= 24 square units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3489562

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Calculating Angle x.a+30+20+20 = 180a = 180-70a = 110°Let 1 unit be the radius of the circle.cos20 = b/1b = cos20b = 0.93969262079 units.c = 2bc = 1.87938524157 units.1.87938524157/sin110 = d/sin40d = 1.28557521937 units.e² = 1.28557521937²+1.87938524157²-2*1.87938524157*1.28557521937cos30e = 1 units.It implies;x+x+20 = 1802x = 180-202x = 160x = 80°

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3488999

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Sir Mike Ambrose is the author of the question.Area blue exactly in cm² is;Area triangle with height (2√(13)-2) cm and base (4sin120) cm.= ½*(2√(13)-2)*(4sin120)= √(3)(2√(13)-2)= 2(√(39)-√(3)) cm²

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