Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/1986629

Let the two equal lengths be 1 unit. (a) Calculating Theta exactly. Let theta be x. Calculating x. x = ½(90-54) x = ½(36) x = 18° sin18 = a/1 a = 0.30901699437 unit. b = 90-18 b = 72° sin72 = c/1 c = 0.9510565163 unit. tan36 = 0.9510565163/d d = 1.30901699437 units. Area Blue is; 0.5(1.30901699437*0.9510565163) = 0.62247457122 square units. e = 270-54-96 e = 120° f = 360-120-72 f = 168° g² = 2-2cos168 g = 1.98904379074 units. h = ½(180-168) h = 6° (1.98904379074/sin54) = (i/sin2...

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Our certified, experienced, resilient, productive and committed Math Educators will be glad to be at your service. We make teaching and learning Mathematics fun for learners, we expose the simplicity and beauty of Mathematics to our learners, and mentor them to appreciate and love Mathematics. Communicate us to mentor/educate you Mathematics better online at affordable tuition. We are smart and clever.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/1985915

Radius of the semi circle is 5 units. Calculating r, radius of the inscribed circle. (5-r)² = 3²+r² 25-10r+r² = 9+r² 10r = 16 r = ⅕(8) units. a = 3-r a = ⅕(7) units. b² = 5²-a² b = ⅕(24) units. c = atan((8/5)/8) c = atan(⅕)° d = 2c d = 2atan(⅕)° tan(2tan(⅕)) = e/(5+(7/5)) e = ⅓(8) units. f = atan(12/5)° g = b-f g = (32/15) units. h² = 50-50cos(180-4atan(⅕)) h = (120/13) units. sin(2atan(⅕)) = (8/3)/i i = (104/15) units. j = h-i j = (448/195) units. k = atan(24/7)° l = (180-atan(2...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/1985499

AE = CF = (12√(2)-12) cm. AE = CF = 4.97056274848 cm. EF = 12√(2)-2(4.97056274848) EF = 7.02943725152 cm. sin60 = a/7.02943725152 a = 6.08767123412 cm. a = height of triangle EFG. It implies; Length BG is; 6√(2)-6.08767123412 = 2.39761014012 cm.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/1985254

Let AB be 1 unit. (1/sin150) = (a/sin20) a = 0.68404028665 units. a is AD. Notice; AB = AC = 1 unit. (CD)² = 1+0.68404028665²-2*0.68404028665cos30 CD = 0.53208888624 units. Therefore, the required angle x is; (0.68404028665/sinx) = (0.53208888624/sin30) x = 40°

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/1985182

Let the radius of the green circle be r. sina = (3+2√(3))/(6+4√(3)) a = asin(½) a = 30° It implies; cos30 = (3+2√(3))/((3+2√(3))+r) 6+4√(3) = 3√(3)+6+√(3)r √(3) = √(3)r r = 1 unit.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/1984724

(3/sin108) = (EG/sin18) EG = 0.9747590887 units. (3/sin108) = (EF/sin54) EF = 2.55195242506 units. AF = 4-2.55195242506 AF = 1.44804757494 units. sin18 = a/1.44804757494 a = 0.44747130932 units. cos18 = b/1.44804757494 b = 1.37717508205 units. b is the height of the trapezoid. Let BJ be x. c = (2-x) units. d² = 1.44804757494²+2²-4*1.44804757494cos108 d = 2.80833171413 units. (2.80833171413/sin108) = (2/sine) e = 42.63384501172° f = 72-42.63384501172 f = 29.36615498828° g² = 3²+2...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/1983938

Let the height and base of the rectangle be x and y respectively. Let the inscribed circle's radius be r. Therefore; 0.5xy = 36 xy = 72 square units. Therefore; y = 72/x --- (1). x = 2r --- (2). Substituting (2) in (1). y = 72/2r y = 36/r units. Let theta be a. tana = x/y tana = 2r/(36/r) tana = (r²/18) --- (3). Calculating r. cos30 = 3/r r = 3/(½√(3)) r = 6/√(3) r = 2√(3) --- (4). Substituting (4) in (3). tan(r²/18), and r is 2√(3) units. tan...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/1982892

Let the radius of the large circle be 1 unit. Diameter of the large circle = 2 units. sin60 = 2/a a = ⅓(4√(3)) units. Where a is the side length of triangle ABC. b² = 2-2cos b = √(3) units. c = a-b c = ⅓(√(3)) units. (d/sin50) = (4√(3)/(3sin100)) d = 1.79639514045 units. e² = (⅓(2√(3)))²+1² e = ⅓√(21) units. 1² = (⅓√(21))²+f²-2*⅓√(21)f cos(atan(3/(2√(3))-10) f² - 2.62161244054f + 1.33333333333 = 0 f = 1.93113 units. g² = 1.93119²+(⅓(4√(3)))²-2*1.93119(⅓(4√(3)))cos10 g = 0.5277832777...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/1980682

Let the regular pentagon side be 1 unit. sin54 = a/1 a = 0.80901699437 unit. b = 2a b = 1.61803398875 units. Let the regular hexagon side be c. Calculating c. c+2(csin30) = b c+2(0.5c) = 1.61803398875 c = 0.80901699437 unit. Calculating Area Yellow. It is; Area regular pentagon with side 1 unit - Half Area regular hexagon with side 0.80901699437 unit - Area triangle with height 1 unit and base sin108 units. = ½(5*1)*(1/(2tan(180/5))) - ½*½(0.80901699437²*6)*(1/(2tan(180/6))) - ½*1*sin...

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