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Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3114832

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a = (r+9) units. b = (r-9) units. a² = b²+c² (r+9)² = (r-9)²+c² c² = r²+18r+81-r²+18r-81 c² = 36r c = 6√(r) units. d = (r+4) units. e = (r-4) units. f²+e² = d² f² = r²+8r+16-r²+8r-16 f = 16r f = 4√(r) units. It implies; g = c-f g = 6√(r)-4√(r) g = 2√(r) units. h = 2r-9-4 h = 2r-13 h = (2r-13) units. j² = h²+g² j² = (2r-13)²+(2√(r))² j² = 4r²-52r+169+4r j² = 4r²-48r+169 j = √(4r²-48r+169) units. Therefore r, radius of the inscribed h...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3114293

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Let r be the radius of the half circle. a²+2² = r² a = √(r²-4) units. b = 2a b = 2√(r²-4) units. c = (r-2) units. Calculating r. √(r²-4) ~ 2√(r²-4) (r-2) ~ 9 Cross Multiply. 9√(r²-4) = (2r-4)√(r²-4) 9 = 2r-4 2r = 13 r = ½(13) units. r = 6.5 units. Recall. b = 2√(r²-4) units. And r = ½(13) units. b = 2√((½(13))²-4) b = 2√(¼(169-16)) b = 2√(¼(153)) b = √(153) units. b = 3√(17) units. tand = 9/(3√(17)) d = atan(3/√(17))° d = 36.0398934303° e =...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3105346

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Calculating angle a. Let the length of the ascribed rectangle be 2 units. Therefore it's width is 1 unit. b² = 2²+1² b = √(5) units. b is the diagonal of the ascribed rectangle. tanc = 1/2 c = atan(½)° tand = 1/0.5 d = atan(2)° e = 2d e = 2atan(2)° f = ½(180-2atan(2)°) f = (90-atan(2))° g² = 2(0.5)²-2(0.5)²cos(2atan(2)) g = 0.894427191 units. h = 90-f-c h = 90-(90-atan(2))-atan(½) h = (atan(2)-atan(½))° h = 36.8698976458° j² = 0.894427191²+√(5)²-2*0.894...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3040149

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Let the side of the regular pentagon be 1 unit. Notice; The regular pentagon side is equal the regular heptagon side. a = ⅐(180*5) a = ⅐(900)°, the single interior angle of the regular heptagon. b = 2a b = ⅐(450)° tan(⅐(450)) = c/0.5 c = 1.03826069829 units. cos(⅐(450)) = 0.5/d d = 1.15238243548 units. Where d is the radius of the ascribed circle. e = 180-⅐(900) e = ⅐(360)° tan18 = 0.5/f f = 1.53884176859 units. g² = 1.15238243548²-0.5² g = 1.03826069828 u...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3002001

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Let GD (inscribed square side) be a. Calculating a. 2(a/(tan60))+a = 12 a = 12/((2/√(3))+1) a = 5.56921938165 cm. b = ½(12-5.56921938165) b = 3.21539030918 cm. Where b is BD = CE. c = 3.21539030918+5.56921938165 c = 8.78460969083 cm. Where c is CD. d² = 3.21539030918²+12²-24*3.21539030918cos60 d = 10.75890566601 cm. Where d is AD. (10.75890566601/sin60) = (12/sine) e = 105° Where e is angle ADB. f = 105-90 f = 15° Where f is angle ADG. cos15 = 5.56921938165/g g = 5.7656801693 cm. Where...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2925743

mathematics-question-and-solution_1736742053n13zqd.jpeg
Let the side of the regular pentagon be 1 unit. Notice; The regular pentagon side is equal the regular heptagon side. a = ⅐(180*5) a = ⅐(900)°, the single interior angle of the regular heptagon. b = 2a b = ⅐(450)° tan(⅐(450)) = c/0.5 c = 1.03826069829 units. cos(⅐(450)) = 0.5/d d = 1.15238243548 units. Where d is the radius of the ascribed circle. e = 180-⅐(900) e = ⅐(360)° tan18 = 0.5/f f = 1.53884176859 units. g² = 1.15238243548²-0.5² g = 1.03826069828 u...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2876016

mathematics-question-and-solution_1734049635Q5konx.jpeg
Let the side of the regular pentagon be 1 unit. Notice; The regular pentagon side is equal the regular heptagon side. a = ⅐(180*5) a = ⅐(900)°, the single interior angle of the regular heptagon. b = 2a b = ⅐(450)° tan(⅐(450)) = c/0.5 c = 1.03826069829 units. cos(⅐(450)) = 0.5/d d = 1.15238243548 units. Where d is the radius of the ascribed circle. e = 180-⅐(900) e = ⅐(360)° tan18 = 0.5/f f = 1.53884176859 units. g² = 1.15238243548²-0.5² g = 1.03826069828 u...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2806591

mathematics-question-and-solution_1730153807vkTZA4.jpeg
Notice. 7 square units is the are of the small pink half circle. ½*a²π = 7 And π = 22/7 ½*a²(22/7) = 7 11a² = 49 √(11)a = 7 a = 7√(11)/11 units. a = 2.110579412 units. a is the radius of the small pink half circle. b = 2a b = 14√(11)/11 units. b = 4.2211588241 units. b is the diameter of the small pink half circle. Let c be the side length of the small square. Calculating c. d = ⅛*180(8-2) d = ⅛*180*6 d = ½*45*6 d = 135° d is the single interior angle of a regu...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2805415

mathematics-question-and-solution_1730103268CkZlfw.jpeg
Notice. 7 square units is the are of the small pink half circle. ½*a²π = 7 And π = 22/7 ½*a²(22/7) = 7 11a² = 49 √(11)a = 7 a = 7√(11)/11 units. a = 2.110579412 units. a is the radius of the small pink half circle. b = 2a b = 14√(11)/11 units. b = 4.2211588241 units. b is the diameter of the small pink half circle. Let c be the side length of the small square. Calculating c. d = ⅛*180(8-2) d = ⅛*180*6 d = ½*45*6 d = 135° d is the single interior angle of a regu...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2797465

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a = 4+6 a = 20 cm. a is the radius of the quarter circle. tanb = 10/4 b = atan(5/2)° c = b+60 c = (60+atan(5/2))° c = 128.1985905136° (10/sin128.1985905136) = (4/sind) d = 18.3215084855° e = 180-d-c e = 180-18.3215084855-128.1985905136 e = 33.4799010009° (10/sin128.1985905136) = (f/sin33.4799010009) f = 7.0195191472 cm. g = 180-atan(5/2)-60 g = (120-atan(5/2))° g = 51.8014094864° Therefore, are blue is; Area quarter circle with radius 10 cm - Area triangle w...
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