Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2693903

Let AB = CD = 1 unit. a = 180-40-30 a = 110° a is angle CAD. (1/sin110) = (b/sin40) b = 0.6840402867 units. b is AC. Therefore, the required angle, x is; (0.6840402867/sinx) = (1/sin30) x = 20°

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2693601

Calculating area shaded blue. a² = (2+√(3))²+(3+2√(3))² a² = 4+4√(3)+3+9+12√(3)+12 a² = 28+16√(3) a = √(28+16√(3)) units. a = 7.4641016151 units. a is the hypotenuse of the ascribed right-angled triangle. Let b be the radius of the inscribed half circle. c = (2+√(3))-b c = (3.7320508076-b) units. d = √(28+16√(3))-(3+2√(3)) d = 7.4641016151-6.4641016151 d = 1 unit. Calculating b. (3.7320508076-b)² = 1²+b² 13.9282032303-7.4641016151b = 1 12.9282032303 = 7.4641016151b...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2693506

Let the side length of the regular octagon be 1 unit. a = ⅛*180(8-2) a = ⅛(180*6) a = 135° a is the single interior angle of the regular octagon. 2b² = 1² b² = ½ b = ½√(2) units. c = 1+b c = (1+½√(2)) units. c is the side length of the square. Therefore, the required angle, x is; tanx = (½√(2))/(1+½√(2)) x = 22.5°

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2693501

Let the side length of the inscribed regular hexagon which is equal the side length of the ascribed regular nonagon be 1 unit. a = ⅙*180(6-2) a = 120° a is the single interior angle of the inscribed regular hexagon. b = ⅑*180(9-2) b = 140° b is the single interior angle of the ascribed regular nonagon. c = 140-120 c = 20° d = 180-20-60 d = 100° (1/sin100) = (e/sin20) e = 0.3472963553 units. (1/sin100) = (f/sin60) f = 0.8793852416 units. g = 1-f g = 0.1206147584 u...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2692696

a = 1+1.5 a = 2.5 units. b²+1.5² = 2.5² b² = 6.25-2.25 b = √(4) b = 2 units. Let c be the radius of the ascribed semi circle. d = 1+2 d = 3 units. e = (3-c) units. f = 1.5+e f = 1.5+3-c f = (4.5-c) units. Calculating c. c² = (4.5-c)²+1.5² c² = 20.25-9c+c²+2.25 9c = 22.5 c = 2.5 units. Again, c is the radius of the ascribed half circle. Therefore, the required length, ?, diameter of the ascribed half circle is; ? = 2c ? = 2*2.5 ? = 5 units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2692646

Let the base of the inscribed green triangle be a. b = (8-a) units. c² = a²+8² c = √(a²+64) units. It implies; (8-a)+8 = √(a²+64) (16-a)² = a²+64 256-32a+a² = a²+64 32a = 192 4a = 24 a = 6 units. Therefore, area green inscribed triangle is; ½*a*8 = ½*6*8 = 24 square units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2692326

Area Orange exactly in fraction is; Area triangle with height. 7.87908624144 units and base 4.37727013143 units + Area triangle with side (38/9) units and 9.01335086564 units, and angle 53.0170930749° = ½(7.87908624144*4.37727013143) + ½((38/9)*9.01335086564)sin53.0170930749 = 17.2444444 + 15.2 = (776/45) + (76/5) = 1460/45 = 292/9 square units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2691721

Let MP be 2 units. a² = 1²+1² a = √(2) units. 2b² = 1² b² = ½ b = ½√(2) units. c = a+b c = ½(3√(2)) units. d² = 1²+(½√(2))²-2*1*½√(2)cos135 d = 1.5811388301 units. Therefore, the required angle, x is; (1.5811388301/sin135) = (0.5√(2)/sinx) x = 18.4349488229°

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2691662

Calculating yellow area. a² = 5²+5²-2*5*5cos120 120° is the single interior angle of the regular hexagon. a = 5√(3) units. a = 8.6602540378 units. tanb = a/(2.5) b = atan(5√(3)/(5/2)) b = atan(2√(3))° b = 73.897886248° b is the angle of the yellow incomplete sector. c² = 2.5²+(5√(3))² c = 8.6746757864 units. d = ½(c) d = 4.3373378932 units. d is the radius of the yellow incomplete sector. e = 90-atan(2.5/(5√(3))) e = 73.897886248° f² = 4.33733789322+5²-2*5*4.33733...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2691653

Let the side length of the three congruent regular hexagon be 1 unit each. Notice. The inscribed green triangle is equilateral. a² = 2-2cos120 120° is the single interior angle of one of the congruent regular hexagon. a = √(3) units. b = 2a b = 2√(3) units. c² = (2√(3))²+1² c² = 13 c = √(13) units. tand = 2√(3)/1 d = atan(2√(3))° e = atan(1/(2√(3)))° f = 120-d f = 46.102113752° It implies; (1/sin60) = (g/sin(atan(2√(3))) g = 1.1094003925 units. (1/sin6...

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