Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2501577

Let R=the bigger inscribed circle radius. Let r=the smaller inscribed circle radius. It implies; R+r=6√(3)-6=4.4 R+r=4.4 -------(1). And the radius of the ascribed semi circle is 6 unit. Calculating the R and r considering the radius of the ascribed semi circle. R=√((6-R)²-R²) Therefore; R=√(36-12R) ----- (2). r=√((6-R)²-R²) Therefore; r=√(36-12r) ----- (3). Adding (2) and (3). R+r=√(36-12R)+√(36-12r)-----(4) Therefore equating (1) and (4). √(36-12R)+√(3...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2500596

a² = 2-2cos120 a = √(3) units. (2/sin30) = (√(3)/sinb) b = 25.6589062733° c = 180-30-b c = 124.3410937267° d² = √(3)²+2²-2*2√(3)cos124.3410937267 d = 3.3027756377 units. e² = 3.3027756377²+1-2*3.3027756377cos60 e = 2.9335219916 units. (2.9335219916/sin60) = (1/sinf) f = 17.1705468636° Therefore, the required angle, Beta is; b+f = 25.6589062733+17.1705468636 = 42.8294531369°

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2500544

Let a be the side length of the regular hexagon. Calculating a. (14/sin60) = (16/sinb) b = 81.7867892983° c = 180-60-b c = 38.2132107017° It implies; (a/sin38.2132107017) = (14/sin60) a = 10 units. Again, a is the side length of the regular hexagon. sin30 = d/a d = 10sin30 d = 5 units. e = 2d+a e = 2(5)+10 e = 20 units. f = e-16 f = 4 units. It implies; (4/sin81.7867892983) = (g/sin38.2132107017) g = 2.5 units. Therefore the required area, area pink...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2500406

Observing similar plane shape (scalene triangle) side length ratios. Therefore; y - 8 20 - 22 It implies; (y/20) = (8/22) (y/20) = (4/11) Cross Multiply. 11y = 80 y = 80/11 units. y = 7.2727272727 units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2500296

3² = 2c²-2c²cos108 108° is the single interior angle of the regular pentagon. It implies; 9 = 2.6180339887c² c² = 3.4376941013 c = 1.8541019663 units. c is the side length of the regular pentagon. sin36 = d/c d = 1.8541019663sin36 d = 1.089813792 units. cos36 = e/c e = 1.8541019663cos36 e = 1.5 units. f = 1.5-1 f = 0.5 units. tang = f/d tang = 0.5/1.089813792 g = atan(0.5/1.089813792) g = 24.6453719079° h = 54-g h = 29.3546280921° j = 180-108-h j = 42.6453719...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2500105

Let the side length of the regular pentagon be 1 unit. a² = 2-2cos108 108° is the single interior angle of the regular pentagon. a = 1.6180339887 units. sin72 = b/1 b = 0.9510565163 units. cos72 = c/1 c = 0.3090169944 units. Area Blue is; 0.5*1*1sin108+0.5*0.3090169944*0.9510565163 = 0.6224745712 square units. d = a-c d = 1.6180339887-0.3090169944 d = 1.3090169943 units. Area Yellow is; 0.5*1.3090169943*0.9510565163 = 0.6224745712 square units. Therefore; Blue Area ÷ Yellow Area is;...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2500086

Let the side length of the regular pentagon be 1 unit. a² = 2-2cos108 108° is the single interior angle of the regular pentagon. a = 1.6180339887 units. Area Blue is; 0.5*1*1.6180339887sin72 = 0.7694208843 square units. Calculating Yellow Area. b = ½(360-2(108)) b = ½(360-216) b = ½(144) b = 72° cos72 = c/1 c = 0.3090169944 units. d² = 0.3090169944²+1²-2*0.3090169944*1cos36 d = 0.7716809592 units. (0.7716809592/cos36) = (0.3090169944/sine) e = 13.6138224422°...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2500064

It implies; 2a² = √(2)² Where a is the radius of the half circle. Therefore; 2a² = 2 a² = 1 a = 1 unit. Again, a is the radius of the half circle. x (diameter of the half circle) is; x = 2a And a = 1 unit. x = 2(1) x = 2 units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2497970

b = (180(12-2))/12 b = 1800/12 b = 150° b is the single interior angle of the regular dodecagon. 2c+2(150) = 360 2c = 60 c = 30° d = 150-15-30 d = 105° 2e+3(150) = 180(5-2) 2e = 540-450 2e = 90 e = 45° f = e-15 f = 30° g = 180-d-f g = 180-105-30 g = 45° It implies; (h/sin105) (2√(2)/sin30) h = 5.4641016151 units. j = 150-15-45 j = 90° k = 180-105-30 k = 45° (l/sin45) = (2√(2)/sin105) l = 2.0705523608 units. l is the side length of the regular dodecagon. m² = 2(2.0705523608)²-2(2.070...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2497946

Let the inscribed square side be 1 unit. sin30 = a/1 a = ½ units. a = 0.5 units. a is the side length of one of the four congruent isosceles inscribed shaded triangle. sin60 = b/1 b = ½√(3) units. c = b-a c = ½√(3)-½ c = ½(√(3)-1) units. c = 0.3660254038 units. d = a+a+c d = 0.5+0.5+½(√(3)-1) d = 1+½(√(3)-1) d = ½(1+√(3)) units. d = 1.3660254038 units. d is the side length of the ascribed square. Shaded Area is; Area square with side 1 unit + 2(area square with side ½ units). = 1²+2(0.5...

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