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Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/1961410

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Let AB = BC = AD = 1 unit. (AC)² = 2-2cos150 AC = 1.93185165258 units. Angle CAB is; = 15° Angle DAC = 90-15 = 75° (CD)² = 1.93185165258²+1-2*1.93185165258cos75 CD = 1.93185165258 units. Notice; CD = AC = 1.93185165258 units. Therefore, the required angle x is; x (angle ADC) = 75°

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/1961338

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Notice, the figure is not drawn to scale. a² = 20²+21² a = √(841) a = 29 units. Therefore; 23+x+3 = 29 x = 29-26 x = 3 units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/1961315

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a = 10√(2) units. a is a diagonal of the square. (12/sin45) = (10√(2)/sinb) b = 56.44269023808° tan56.44269023808 =10/c c = 6.63324958071 units. d = 10-6.63324958071  d = 3.36675041929 units. d is adjacent length (base) of the blue inscribed right-angled triangle. e = 90-56.44269023808 e = 33.55730976192° f = 90-33.55730976192-45 e = 11.44269023808° tan11.44269023808 = f/10 f = 2.02410864032 units. g = 10-2.02410864032 g = 7.97589135968 units. g is adjacent length...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/1961055

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The radius of the inscribed circle is 2 units. a = 2atan(⅓)° b = 2atan(⅕)° c = 180-a-b c = (180-2atan(⅓)-2atan(⅕))° sin(2atan(⅓)) = d/16 d = (48/5) units. cos(2atan(⅓)) = e/16 e = (64/5) units. f = (90-2atan(⅓)-2atan(⅕))° tan(90-2atan(⅓)-2atan(⅕)) = g/(48/5) g = (198/35) units. Therefore; Area Blue exactly in square units is; ½*(48/5)(198/35) = 4752/175 square units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/1961051

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8 = 4 a = (8-a) Cross multiply. 64-8a = 4a 64 = 12a a = ⅓(16) cm. b = 8-a b = ⅓(8) cm. c = atan(⅔)° d = atan(3/2)° ⅔ = 8/e e = 12 cm ⅔ = f/8 f = ⅓(16) cm. g = 8-f g = ⅓(8) cm. Area Orange exactly in cm² is; Area square units side 8 cm - Area rectangle with length 4 cm and width ⅓(8) cm. = 8² - 4*⅓(8) = 64 - ⅓(32) = ⅓(192-32) = ⅓(160) cm²

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/1960663

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Let AB be 1 unit. a = 180-24-45 a = 111° a is angle AED. (1/sin111) = (b/sin24) b = 0.43567391896 units. b is ED. c = √(2) units. c is BD. d = √(2)-0.43567391896 d = 0.97853964341 units. d is BE. (CE)² = 0.97853964341²+1-2*0.97853964341cos45  CE = 0.75741388863 units. (0.75741388863/sin45) = (0.97853964341/sine) e = 66° e is angle ECB. f = 90-66 f = 24° f is angle DCE. g = 90+24 g = 114° g is angle ECF. Therefore, the required angle x is; 180-114-24 = 42°

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/1960629

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Let the square side be 2 units. tan30 = a/2 a = 2/√(3) units. a is BK. b = 2-a b = (2-(2/√(3))) units. b is CK. tan30 = (2-(2/√(3)))/c c = (2√(3)-2) units. c is CM. d = 2-c d = 2-(2√(3)-2) d = (4-2√(3)) units. d is DM. Therefore, the required angle x is; tanx = ½(4-2√(3)) x = atan(½(4-2√(3))) x = 15°

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/1960597

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Let AB = CD = 2 units. Let the big inscribed square side length be a. Considering similar triangle ratios, calculating a. (a-2) = (2+a)       2 = a Cross Multiply. a²-2a = 4+2a a²-4a-4 = 0 (a-2)² = 4+4 a = 2±2√(2) a ≠ 2-2√(2) units. a = 2+2√(2) units. Again, a is the big inscribed square side length. BC = a-AB BC = 2+2√(2)-2 BC = 2√(2) units. Notice; Area Blue is; 2² = 4 square units. Area red is; ½*2*2√(2) = 2√(2) units. It implies; Area Red ÷ Area Blue is; 2√(2)÷4 = ½√(2)

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/1960512

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Let the square side be 2 units. a = atan(2) b = (180-atan(2))° (2/sin(180-atan(2))) = (1/sinc) c = 26.56505117708° d = 180-(180-atan(2))-26.56505117708 d = 36.86989764584° e = 90-2d e = 90-2*36.86989764584 e = 16.26020470832° Therefore, calculating b. b² = 8-8cos16.26020470832  b = 0.56568542495 units. Calculating a. a² = 8-8cos36.86989764584 a = 1.26491106407 units. Therefore; a : b is; 1.26491106407 : 0.56568542495 = 1.26491106407÷0.56568542495 = 2.2360679775  = √(5)

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/1958696

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Calculating green area. a² = 5²+5² a = √(50) a = 5√(2) units. b = ½(a) b = ½(5√(2)) units. b = 3.53553390593 units. 5² = (5-c)²+(½(5√(2)))² 25 = 25-10c+c²+¼(50) c²-10c+¼(50) = 0 4c²-40c+50 = 0 Notice;  c is the radius of the green circle. c = 1.46447 units. Therefore; Green area is; π(1.46447)² = 6.73768699619 square units. Calculating blue area. d = 5-1.46447 d = 3.53553 units. e = 45° f = ½(e) f = 22.5° tan22.5 = g/5 g = 2.07106781187 units. Ar...
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