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Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2811317

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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 units. b = 90-18 b = 72° sin72 = c/1 c = 0.9510565163 units. 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...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2811310

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Let the side of the inscribed square be a. Calculating a. a+2√(a²-(a/2)²) = 10√(2) a+2√(3a²/4) = 10√(2) 2√(3a²/4) = 10√(2)-a 3a² = 200-20√(2)a+a² 2a²+20√(2)a-200 = 0 a²+10√(2)a-100 = 0 (a+5√(2))² = 100+50 a = -5√(2)±5√(6) It implies; a ≠ -5√(2)-5√(6) a = 5(√(6)-√(2)) a = 5.17638090205 cm. b² = a²-(a²/4) b = 4.48287736084 cm. Shaded area is; a²+(a*b) = 5.17638090205²+(5.17638090205*4.48287736084) = 26.79491924311 + 23.20508075689  = 50 cm²

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2809745

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Sir Mike Ambrose is the author of the question. Biggest square side is 14 units. Bigger square side is 8 units. a = atan(9/16) (9/16) = b/c c = (16b/9) units. (16b/9)+6 = 14 (16b/9) = 8 b = (9/2) units. c = (16*9/2)/9 c = 8 units. d = 9-b d = (9/2) units. Where d is the side length of the big square. Or (9/16) = d/8 d = (9/2) units. (e/sin(atan(9/16))) = (8/sin(180-atan(9/16)-atan(9/6)) e = 12√(13)/11 units. f² = e²+(9/2)²-9ecos(90+atan(2/3)) f = 7.4402...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2809727

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Sir Mike Ambrose is the author of the question. Area Red Total in 1 d. p. Square unit is; Area Square with side 2√(2) units - Area triangle with height 2√(2) units and base 1.1313708499 units + Area triangle with two side √(13) units and 3.28571428572 units, and angle atan(3/2)° = (2√(2))² - 0.5*2√(2)*1.1313708499 + 0.5*√(13)*3.28571428572sin(atan(3/2)) = 8 - 1.6 + 4.92857142858 = 11.3285714286 ≈ 11.3 square units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2808401

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Let the biggest regular pentagon side length be 2 units. sin72 = a/2 a = 1.90211303259 units. tan72 = (1.90211303259/b) b = 0.61803398875 units. c = 2b c = 1.2360679775 units. Where c is the side length of the regular red and blue pentagon. Calculating area of the regular red and blue pentagon. (5*1.2360679775²)/(4tan36) = 2.6286555606 square units. d² = 8-8cos108 d = 3.2360679775 units. e = ½(3.2360679775-c) e = 1 unit. f² = 8-8cos36 f = 1.2360679775 units....

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2808389

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Sir Mike Ambrose is the author of the question. The side length of the congruent Hexagons is 2 units. Area hexagon is; (6*2²)/(4tan30) = 6√(3)) square units. a² = 8-8cos30 a = √(8-4√(3)) units. Area ABC is; ½(√(8-4√(3)))²sin60 = (2√(3)-3) square units. (d) Area Hexagon ÷ Area ABC exactly is; (6√(3)) ÷ (2√(3)-3) = 6(2+√(3)) (c) Calculating Area Green to 2 decimal places. b = a + √(2²+2²) b = √(8-4√(3))+2√(2) b = (√(2)+√(6)) units. b = 3.86370330516 units. ...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2806638

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Let the side length of the regular pentagon be 4 units. a = ⅕*180(5-2) a = 108° a is the single interior angle of the regular pentagon. b = ½(180-a) b = ½(180-108) b = 36° c = 2 units. d = 90-36 d = 54° tan54 = e/2 e = 2.7527638409 units. Area yellow is; 0.5*2*2.7527638409 = 2.7527638409 square units. Calculating area regular pentagon. f² = 4²+4²-2*4*4cos108 f = 6.472135955 units. g = 108-90 g = 18° sin18 = h/4 h = 1.2360679775 units. cos18 = j/4...

Mathematics Question and Solution

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

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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/2805677

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a² = 4²+3² a = √(25) a = 5 units. a is MN, the side length of the inscribed square. b² = 2(5²) b = 5√(2) units. b is MK, the diagonal of the inscribed square. tanc = 4/3 c = atan(4/3)° c is angle ALK. d = atan(3/4)° d is angle CLM. e = ½(90)+d e = (45+atan(3/4))° e is angle CLN. f = 180-45-e f = 135-(45+atan(3/4)) f = 90-atan(3/4) f = atan(4/3)° f is angle CNL. Calculating x (CL). (x/sin(atan(4/3))) = (5√(2)/sin45) x = 8 units.

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...
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