Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2477288

Notice, triangle ABC is isosceles. Let BC, the base of triangle ABC = 1 unit. a = ½(180-45) a = ½(135) a = 67.5° a is angle ABC = angle ACB. b = a-45 b = 22.5° b is angle DBE. c = a-30 c = 37.5° c is angle BCD. d = 180-45-67.5 d = 67.5° d is angle BEC. (1/sin67.5) = (e/sin45) e = 0.7653668647 units. e is CE. f = 180-67.5-37.5 f = 180-105 f = 75° f is angle BDC. (1/sin75) = (g/sin67.5) g = 0.9564704736 units. g is CD. h² = 0.9564704736²+0.7653668647²-...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2477130

Let x be the single interior angle of the regular polygon. a = 180-x-20 a = (160-x)° b = 180-x-30 b = (150-x)° c = 180(5-2) c = 540° d = 2(360-x)° It implies;. a+b+d+86 = c (160-x)+(150-x)+2(360-x)+86 = 540 396+720-4x = 540 1116-540 = 4x 4x = 576 x = 144° Again, x is the single interior angle of the regular polygon. Calculating n, number of sides of the regular polygon. Sum = 180(n-2) And Sum = xn, where x = 144° It implies; 144n = 180n-360 180n-144n = 360...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2476573

Area Blue is; Area semi circle with radius √(2) units - Area quarter circle with radius 2 units + Area triangle with height and base 2 units respectively. = ½(√(2)²)π - ¼(2²)π + ½(2²) = π - π + 2 = 2 square units

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2476565

Area Blue is; Area triangle with height 4 cm and base (4sin150) cm = ½*4*(4sin150) = 2(4sin150) = 8sin150 = ½(8) = 4 cm²

Mathematics Question and Solution

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

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

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

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

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

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

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...

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