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Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/1859384

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Let the forward diagonal of the quadrilateral be 2 units. (2/sin110) = (a/sin35) a = 1.22077458876 units. (b/sin30) = (2/sin55) b = 1.22077458876 units. It implies; x = ½(180-130) x = 25°

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/1858604

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Let the base of the ascribed triangle be 1 unit. a = 180-3-6 a = 171° (1/sin171) = (b/sin3) b = 0.33455515209 units. c = 180-30-87 c = 63° (1/sin63) = (d/sin30) d = 0.56116311882 units. e² = 0.56116311882²+0.33455515209²-2*0.33455515209*0.56116311882cos81 e = 0.60670683106 units. Calculating angle x. (0.60670683106/sin81) = (0.33455515209/sinx) x = 33.00000000025° x = 33°

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/1855059

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Calculating BC. (BC/sin30) = (12/sin75) BC = 6.21165708246 cm. Calculating EF. (6.21165708246/sin75) = (EF/sin30) EF = 3.21539030917 cm. Angle FEG is; 360-2(75)-60 = 360-210 = 150° It implies; Area triangle EFG is; 0.5*3.21539030917*3.21539030917sin150 = 2.58468371008 cm²

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/1855044

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Let the radius of the circle be r. Calculating r. √(r²-4)+√(r²-1) = 3 r²-4 = (3-√(r²-1))² r²-4 = 9-6√(r²-1)+r²-1 6√(r²-1) = 12 √(r²-1) = 2 r = √(5) units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/1854583

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BC = √(3²+4²) BC = 5 cm. tana = (4/3) a = atan(4/3)° tan(½(atan(4/3))) = AF/3 AF = 3tan(½(atan(4/3))) AF = 1.5 cm. b = 90-½(atan(4/3)) b = 63.43494882292° Where b is angle AFE. sin63.43494882292 = AE/1.5 AE = 1.3416407865 cm. (BE)² = 3²-1.3416407865² BE = 2.683281573 cm. Calculating Length CE. (CE)² = 5²+2.683281573²-2*5*2.683281573cos(0.5atan(4/3))  CE = 2.86356421266 cm. (2.683281573/sinc) = (2.86356421266/sin(0.5atan(4/3))) c = 24.77514056879° Where c is angle BCE. Angle ECF = atan...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/1854240

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Calculating r, radius of the circle. r² = (r-3)²+4² r² = r²-6r+9+16 6r = 25 r = (25/6) units. a = r-3 a = (25/6)-3 a = (25-18)/6 a = (7/6) units. tanb = (7/6)/4 b = atan(7/24)° c = 180-b c = (180-atan(7/24)° c = 163.73979529169° Therefore; AB Length is; (AB)² = (25/6)²+3²-2(25/6)*3cos163.73979529169 (AB)² = 1813/36 AB = √(1813/36) AB = 7√(37)/6 units. AB = 7.09655628535 units. Or  Length AB is; (AB)² = (r-3)²+7² And r = (25/6) units. (AB)² = ((25/6)-3)²+49 (AB)² = (7/6)²+49 (AB)² = (49...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/1852092

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Let r be the radius of the semi circle. Calculating r. √(r²-49)+√(r²-36) = 12 r²-49 = (12-√(r²-36))² r²-49 = 144-24√(r²-36)+r²-36 24√(r²-36) = 144+13 24√(r²-36) = 157 r²-36 = (157/24)² r² = (157/24)²+36 r² = 45385/576 r = √(45385/576) r = √(45385)/24 units. r = 8.87656480728 units  Green Area is; Area semi circle with radius 8.87656480728 units - Area inscribed rectangle with length and width 12 units and 6 units respectively. = 0.5(45385/576)π-(12*6) = (45385/1152)π-72 = (45385π-82944)...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/1851945

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Angle DAG = 60-45 = 15° Angle DAG = Angle DCF  = 15° Angle CDF = 90-15 = 75° Angle ADG = 90-75 = 15° It implies; Triangle ADG is an isosceles. Calculating DG. cos15 = 6/(DG) DG = 6/cos15 DG = 6(√(6)-√(2)) cm. DG = 6.21165708246 cm.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/1851891

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tanx = 2/a a = 2/tanx ----- (1). b = a+2 b = (2/tanx) + 2 ----- (2). Notice; a = the short adjacent length of the right-angled triangle. b = the long adjacent length of the right-angled triangle. Let tanx = c. Calculating the hypotenuse of the right-angled triangle. (2/c)-2+(2/c) = (4/c)-2 = (4-2c)/c units. It implies; Using sum of areas derived that are inscribed the ascribed triangle to equal the area of the ascribed triangle to find c. 2(2/c)+2(2c+2)/c+2(4-...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/1851676

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Let the height of the triangle be a. Let angle alpha be b. tanb = 3/a ----- (1) tan2b = 8/a ----- (2) And tan2b = 2tanb/(1-tan²b) Therefore; 2tanb/(1-tan²b) = 8/a ----- (3) Substituting (1) in (3). (2*(3/a))/(1-(3/a)²) = 8/a (6/a)/(1-(9/a²)) = 8/a (6/a)/((a²-9)/a²) = 8/a (6a/(a²-9)) = 8/a 6a² = 8a²-72 2a² = 72 a² = 36 a = 6 units. Notice, a is the height of the triangle. Therefore x is; √(6²+8²)  = √(100) = 10 units.
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