Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3204947

Calculating angle x. a = 180-2(48) a = 180-96 a = 84° b = 180-72-a b = 180-72-84 b = 180-156 b = 24° c = ½(180-72) c = ½(108) c = 54° d = 90-c d = 90-54 d = 36° Therefore, the required angle x is; x+b+d = 180 x+24+36 = 180 x = 180-60 x = 120°

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3204652

Calculating Area Blue. a = 5+3 a = 8 units. a is the side length of the big square. b² = 3²+8² b² = 9+64 b = √(73) units. c = ½(b) c = ½√(73) units. c is the side length of the two equal small squares. tand = (3/8) d = atan(3/8)° e = 90-45-d e = (45-atan(3/8))° e = 24.4439547804° f² = 2(½√(73))² f² = 2*¼(73) f = √(½*73) f = 6.0415229868 units. f is the diagonal of each of the two equal small squares. Area Blue is; ½*a*fsine = 0.5*8*6.0415229868sin24.443...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3203679

Calculating Shaded Area Blue. a² = 4²+3² a = √(25) a = 5 units. a is the radius of the quarter circle. 5 ~ 4 3 ~ b Cross Multiply. 5b = 12 b = 2.4 units. d² = 5²+3² d = √(34) units. tane = 3/4 e = atan(¾)° f² = 4²+2.4² f = 4.66476151588 units. g = d-f g = 1.16619037897 units tanh = 4/2.4 h = atan(5/3)° j = 180-h j = (180-atan(5/3))° Area Blue is; (0.5*2.4*1.16619037897sin(180-atan(5/3)))+(atan(3/4)π*5²÷360)-(0.5*5²sin(atan(3/4)) = 1.2+8.043763859...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3203677

Let 1 unit be AB = BC = CD. a² = 2-2cos150 a = 1.93185165258 units. a is BD. b = 90-½(180-150) b = 90-15 b = 75° b is angle ABD. c² = 1+1.93185165258²-2*1.93185165258cos75 c = 1.93185165258 units. Notice. AD = BD Therefore, the required angle, angle ADC is; 15+(180-2(75)) = 15+(180-150) = 15+30 = 45°

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3202632

Sir Mike Ambrose is the author of the question. Calculating Area Shaded ÷ Area Purple to 2 decimal places. Let AB be 5 units. Radius, r of the inscribed circle is; r = 5*(2/5) r = 2 units. a = ⅛(180*6) a = 135° 2b² = 25 b = ½(5√(2)) units. c = 180-0.5(135)-45 c = 67.5° sin22.5 = ½(5√(2))/d d = 9.23879532511 units. Where d is the side length of the regular triangle (purple area). Area purple is; 0.5*9.23879532511*9.23879532511sin60 = 36.95994598698 square...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3202538

Calculating Area Blue. a = 5+3 a = 8 units. It implies; b*4 = 3*8 4b = 24 b = 6 units. b is BC. c = 4+b c =10 units. d² = 10²+5² d² = 125 d = √(125) d = 5√(5) unit. d is the diameter of the ascribed circle. e = ½(d) e = ½(5√(5)) units. e = 5.59016994375 units. e is the radius of the ascribed circle. tanf = 3/6 f = atan(½)° tang = 5/10 g = atan(½)° h = f+g h = 2atan(½)° j = 180-2h j = (180-4atan(½))° j = 73.7397952917° Area Blue is; Area sec...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3202296

Calculating area of the circle. Let the radius of the circle be r. Therefore; (2r)²=2(√(20))² 4r²=40 r = √(10) units. Therefore area of the circle is; π√(10)² = 10π square units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3202289

Calculating R, radius of the inscribed circle. Let a be the radius of the inscribed half circle. Calculating a. b²+9² = 15² b² = 225-81 b = √(144) b = 12 units. c = (12-a) units. d = (9-a) units. It implies; (12-a) ~ a a ~ (9-a) Cross Multiply. a² = 108-21a+a² 21a = 108 7a = 36 a = ⅐(36) units. Or 12a+9a = (12*9) 21a = 108 a = ⅐(36) units. Recall. c = (12-a) And a = ⅐(36) units. c = 12-⅐(36) c = ⅐(84-36) c = ⅐(48) units. tane = 9/12 e = at...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3201721

Calculating the inscribed angle beta, let it be y. Let (x+3) units be the side length of the square. a²+x² = 4² a = √(16-x²) units. b = 1+a b = (1+√(16-x²)) units. b is the side length of the square. Notice. b = (x+3) units as well. Therefore; Calculating x. It implies; x+3 = 1+√(16-x²) (x+2)² = 16-x² x²+4x+4 = 16-x² 2x²+4x-12 = 0 x²+2x-6 = 0 (x+1)² = 6+(1)² (x+1)² = 7 x = -1±√(7) It implies; x ≠ -1-√(7) units. x = (√(7)-1) units. x = 1.64575131106 u...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3201150

Sir Mike Ambrose is the author of the question. Calculating Area Blue exactly in square units. Area Blue is; Area triangle with two side length 10½ units and ((7√(5)sin(atan(3/4)))/(2sin(180-atan(2)-atan(3/4))) units respectively, and angle (180-2atan(2))°, the angle they form. = ½(21/2)((7√(5)sin(atan(3/4)))/(2sin(180-atan(2)-atan(3/4)))sin(180-2atan(2)) = ¼(21)(378/99) = ½(441/11) = (441/22) square units.

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