Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3209217

Calculating angle x. a = 180-2(58)-48 a = 180-116-48 a = 180-164 a = 16° a is angle BAD. Let 1 unit be the let AB equal length AC. (a')² = 2-2cos(a+48) a' = √(2-2cos64) a' = 1.05983852847 units. a' is length BC. b = 180-48-58-30 b = 180-136 b = 44° b is angle ADC. (c/sin48) = (1/sin44) c = 1.06979899341 units c is length CD. (d/sin(58+30)) = (1/sin44) d = 1.43867960068 units. d is length AD. e² = 1+1.43867960068²-2*1.43867960068cos16 e = 0.55127471164 units...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3209215

Calculating Area Inscribed Green Circle. Let a be the radius of the inscribed green circle. b = 8-2 b = 6 units. tanc = 6/8 c = atan(3/4)° d = ½(90+c) d = ½(90+atan(3/4))° e = (2-a) units. It implies; tan(½(90+atan(3/4))) = a/(2-a) 2 = a/(2-a) 4-2a = a 3a = 4 a = ⅓(4) units. Again, a is the radius of the inscribed green circle. Therefore, area inscribed green circle is; πa² = π(4/3)² = ⅑(16π) square units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3207724

Calculating Required Shaded Area. Notice. The three circles are congruent. Therefore, the required shaded area is; Area equilateral triangle with side r units+3(area sector with radius r units and angle 60° - area regular triangle with height r units and base rsin60 units). = 0.5r²sin60+3((60π*r²/360)-(0.5r²sin60)) = ¼√(3)r²+3(⅙(πr²)-¼√(3)r²) = ¼√(3)r²+½(πr²)-¾√(3)r² = ½(πr²)-½√(3)r² = ½(π-√(3))r² square units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3207712

Sir Mike Ambrose is the author of the question. Calculating Area Blue. It is; Area triangle with height 25 units and base ⅓(100) units - Area square with single side length 5 units - Area triangle with height 30 units and base 30tan(atan(5/35)) units - Area triangle with height 5 units and base ⅓(20) units - Area triangle with height 5 units and base 25sin(atan(3/4)) units. = ⅓(1250) -25 - 450tan(atan(5/35)) - ⅓(50) - ½(75) = ½(675) - 450tan(atan(5/35)) = ½(675 - 900tan(ata...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3207702

Calculating yellow area. Notice. Area of the ascribed square is 12 square units. Area yellow is; ½(12) - (½(⅔√(3))²sin(atan(3))÷sin(135-atan(3)))sin(45) = 6 - (½) = ½(12-1) = ½(11) square units. = 5.5 square units. Or Calculating Yellow Area. Let a be the side length of the square. a² = 12 a = √(12) = 2√(3) units. a = 3x x = ⅓(2√(3)) units. x = 1.15470053838 units. tanb = 3x/x b = atan(3)° b = 71.5650511771° c = 180-45-b c = 180-45-71.5650511771...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3206769

Calculating Area Rectangle. Let r be the radius of the half circle and also, the width of the rectangle. a = r+r a = 2r units. a is the diameter of the half circle. b = (2r-x) units. b is the length of the rectangle. c = ½(6) c = 3 units. It implies; r ~ 6 3 ~ (2r-x) Cross Multiply. (2r-x)r = 18 Notice. (2r-x)r is the length times the width of the rectangle (area rectangle). Therefore; Area rectangle = 18 square units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3206420

Sir Mike Ambrose is the author of the question. Let the single side length of the regular hexagon be 2 units. Area rectangle is; 2.5x√(3) = ½(5√(3)) square units. Area green is; Area trapezoid with two parallel side length 3 units and height √(3) units - Area triangle with height (√(3)/3) units and base 1 unit. =½(3√(3)) - ½(√(3)/3)) = (4√(3)/3) square units. It implies; Area Green ÷ Area Rectangle exactly in its simplest form is; (4√(3)/3) ÷ ½(5√(3)) = (8√(3...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3206416

Calculating Area Green. Let x be the side length of the ascribed square. a = ½(x) units. tanb = x/(½(x)) b = atan(2)° c = 180-45-atan(2) c = (45+atan(½))° It implies; (0.5x/sin(45+atan(½))) = (d/sin(atan(2))) d = 0.47140452079x units. Calculating x. 0.5*0.47140452079x*0.5xsin45 = 12 0.47140452079a² = 48√(2) x = √(48√(2)/0.47140452079) x = 12 units. Again, x is the side length of the ascribed square. It implies; 0.5*(0.5*12)*e = 12 6e = 24 e = 4 units....

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3205271

Calculating Angle x. Let AC = 1 units. sin(10+10) = a/1 a = 0.34202014333 units. a is BC. tan40 = b/0.34202014333 b = 0.28698897612 units. c = 180-10-30-40 c = 100° (1/sin100) = (d/sin10) d = 0.17632698071 units. e = a-d e = 0.34202014333-0.17632698071 e = 0.16569316262 units. Therefore, the required angle x is; tanx = e/b x = atan(0.16569316262/0.28698897612) x = 30°

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3204969

Calculating Yellow Area. 2a² = 2² a = √(2) units. a is the radius of each of the two congruent half circles. 2b² = (2+1)² b² = ½(9) b = ½(3√(2)) units. b is the radius of the circle. c = a+b c = √(2)+½(3√(2)) c = ½(5√(2)) units. It implies; (½(5√(2)))² = (½(3√(2))²+d² ½(25) = ½(9)+d² 2d² = 25-9 2d² = 16 d² = 8 d = 2√(2) units. e = d-a e = 2√(2)-√(2) e = √(2) units. f = 2(d) f = 4√(2) units. Therefore, yellow area is; ½*3*4√(2)sin45 = ½(12) = 6 s...

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