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Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2476458

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Sir Mike Ambrose is the author of the question. sin30 = (4√(3))/a a = 8√(3) units. a is AC. AB = ⅓(a) AB = ⅓(8√(3)) units. cos30 = b/⅓(8√(3)) b = ⅓(8√(3))*½√(3) b = 4 units. sin30 = c/⅓(8√(3)) c = ⅓(4√(3)) units. d = 4+b d = 8 units. tan60 = e/8 e = 8√(3) units. cos60 = 8/f f = 16 units. Let r be the radius of the inscribed circle. 16r+8r+8√(3)r = 8*8√(3) (24+8√(3))r = 64√(3) r = (4√(3)-4) units. r = 2.9282 units. g = r+c g = (4√(3)-4)+⅓(4√(3)) g = ⅓(...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2475211

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Calculating angle x, observing sine rule. (80/sin(2x)) = (50/sinx) 80sinx = 50sin(2x) 8sinx = 10sinxcosx 4 = 5cosx x = acos(4/5) x = 36.8698976458° Therefore; Angle 2x is; 2*36.8698976458 = 73.7397952917° It implies: a+2x+x = 180 a = 180-73.7397952917-36.8698976458 a = 69.3903070626° Therefore, area triangle is; 0.5*50*80sin69.3903070626 = 1872 square units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2473866

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Observing similar plane shape (right-angled) side length ratios. (6+x) - (6+2+6)        6 - 8 Cross Multiply. 8(6+x) = 6(14) 48+8x = 84 8x = 84-48 8x = 36 x = ½(9) units. Again; Observing similar plane shape (right-angled) side length ratios. 6 - y (6+½(9)) - ½(9) Cross Multiply. 27 = 10.5y 27 = ½(21)y y = (2*27)/21 y = ⅐(18) units. Shaded Area Pink is; ½(xy) = ½*½(9)*⅐(18) = (81/14) square units. = 5.7857142857 square units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2473449

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Calculating R, radius of the small inscribed quarter circle. a = 2*18 a = 36 units. a is the radius of the ascribed quarter circle. b = (18+R) units. It implies; R, radius of the small inscribed quarter circle is; 36² = R²+(18+R)² 1296 = R²+324+36R+R² 2R²+36R-972 = 0 R²+18R-486= 0 Resolving the above quadratic equation. R = (9√(7)-9) units. R = 14.8118 units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2473303

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sin60 = 18/a a = 20.7846096908 units. tan60 = 18/b b = 10.3923048454 units. c+270+60+30+135 = 180(5-2) c = 540-495 c = 45° d² = 2(18²) d = 18√(2) units. d = 25.4558441227 units. e = a+d e = 20.7846096908+25.4558441227 e = 46.2404538135 units. f = (85+z) units. f is the required length x. Therefore: x = f = (85+z) units. g = (46.2404538135+z) units. tan60 = h/a h = 20.7846096908tan60 h = 36 units. j = (25.4558441227+z) units. j is the required length y. y...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2473210

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sin75 = a/30 a = 28.9777747887 units. cos75 = b/30 b = 7.7645713531 units  cos75 = c/15 c = 3.8822856765 units. d = 15-c d = 11.1177143235 units. Area Orange is; Area rectangle with length 28.9777747887 units and width 11.1177143235 units - Area sector with radius 15 units and angle 150° + Area triangle with radius 15 units and angle 150° = (28.9777747887*11.1177143235)-((150π*15*15)/360)+(0.5*15*15sin150) = 83.8923105574 square units. = 83.89 square units to 2 decimal...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2473184

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15² = a²+6² a² = 225-36 a = √(189) a = 3√(21) units. b = 2a b = 6√(21) units. sin75 = c/b c = 6√(21)sin74 c = 26.5585692881 units  d = 10+c d = 36.5585692881 units. cos75 = e/(6√(21)) e = 7.1163471929 units. sinf = 6/15 f = 23.5781784782° g = 75-f g = 51.4218215218° h = 180-2g h = 77.1563569564° j² = 2*15²-2*15²cos77.1563569564 j = 18.7074571083 units. k = 15-½(j) k = 5.6462714458 units. l = k+5+j-e l = 22.2373813613 units. m = j-e m = 18.7074571...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2471810

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Shaded Area is; Area circle with diameter 30 cm - 7(area circle with diameter 10 cm) = π(½(30))² - 7π(½(10))² = π(15)² - 7π(5)² = 225π - 175π = 50π cm²

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2471583

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Sir Mike Ambrose is the author of the question. Let CD = 2 units. Therefore; Calculating AB. AB = 1 + (2sin18*tan72 + 2sin36)tan54 AB = 1 + 3.07768353717tan54 AB = 1 + 4.23606797749 AB = 5.23606797749 units. It implies; Length AB ÷ Length CD to 2 decimal places is  5.23606797749 ÷ 2 = 2.61803398874  ≈ 2.62

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2470996

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x² = (r+1)² - (r-1)² Therefore x = 2√(r) unit. y² = (r+1)² - (2√(r))² Therefore y = √(r²-2r+1) y = √(r-1)² y = (r-1) unit. z = (r+1) - y z = (r+1) - (r-1) Therefore z = 2 units. a = r+r Therefore a = 2r units. A sincere study and analysis of the composite circles deduced a right-angled triangle with two adjacent sides, 2 units and 2√(r) units respectively, and hypotenuse 2r units. Therefore; Calculating r, the radius of the three congruent circles. (2r)² = 2² + (2√(r))² 4r² = 4 + 4r 4r²...
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