Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2437851

Let the side length of the regular pentagon be 1 unit. a = ⅕(180(5-2)) a = 108° a is the single interior angle of the regular pentagon. b² = 2-2cos108 b = 1.6180339887 units. c = ½(180-108) c = 36° d = 108-36 d = 72° e = 180-72-30 e= 78° (1.6180339887/sin78) = (f/sin30) f = 0.8270909153 units. g = 180-78 g = 102° Therefore, the required angle alpha is; Let it be h. (1/sin102) = (0.8270909153/sinh) h = 54°

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2428076

Let the side length of the regular hexagon be 2 units. a = ⅙(180(6-2)) a = 120° a is the single interior angle of the regular hexagon. b² = 2²+1²-2*2*1cos120 b = √(7) units. b = 2.6457513111 units. (2.6457513111sin120) = (1/sinc) c = 19.1066053509° d = 120-c d = 120-19.1066053509 d = 100.8933946491° Therefore, e is; e = 0.5*√(7)*2cos100.8933946491 e = √(7)cos100.8933946491 e = 2.5980762114 square units. e is the area of green plus orange inscribed plane shape (inscribed scalene triangle)...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2427217

a² = 10²+5² a = √(125) a = 5√(5) units. a = 11.1803398875 units. a is the side length of the square. tanb = 10/5 b = atan(2)° c = atan(1/2)° d = 45-c d = (45-atan(1/2))° d = 18.4349488229° e = 45+d e = 45+(45-atan(1/2)) e = 45+18.4349488229 e = 63.4349488229° e = atan(2)° sine = f/10 sin(atan(2)) = f/10 f = 8.94427191 units cose = g/10 cos(atan(2)) = g/10 g = 4.472135955 units. h = a-g h = 5√(5)-4.472135955 h = 6.7082039325 units. j = f-g j = 8.94427191-4.472135955 j = 4.472135955 uni...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2426678

Calculating R, radius of the circle. It implies; 10²+11²-2*10*11cosa = 7²+8²+2*7*8cosa 221-220cosa = 113+112cosa 221-113 = 112cosa+220cosa 108 = 332cosa cosa = 108/332 a = acos(108/332) a = 71.016175615° b² = 10²+11²-2*10*11cos71.016175615 b = 12.2243091805 units. Therefore, R, radius of the circle is; sin71.016175615 = (0.5*12.2243091805)/R R = (0.5*12.2243091805)/sin71.016175615 R = 6.4637130226 units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2421406

a² = 30²+10²-2*30*10cos120 a = 36.0555127546 cm. (36.0555127546sin120) = (30/sinb) b = 46.1021137521° cosb = 10/d Where d is PQ. cos46.1021137521 = 10/d d = 10/cos46.1021137521 d = 14.4222051019 cm.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2406880

a = ⅕(180(5-2)) a = 108° b = 180-108 b = 72° sin72 = c/6 c = 5.7063390978 cm. cos72 = d/6 d = 1.8541019662 cm. e = 1.8541019662+6 e = 7.8541019662 cm f² = 7.8541019662²+6²-2*7.8541019662*6cos108 f = 11.2610625384 cm. (11.2610625384/sin108) = (6/sing) g = 30.4463843172° h = 90-30.4463843172 h = 59.5536156828° i = 180-18-59.5536156828 i = 102.4463843172° (5.7063390978/sin102.4463843172) = (j/sin59.5536156828) j = 5.0378552605 cm. k² = 6²+6²-2*6*6cos108 k = 9.7082039325 cm. l = 90-18 l...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2403454

Let the diameter of the inscribed circle be 1 unit. Therefore, the radius of the ascribed semi circle is 1 unit. Calculating angle a°. b = 0.5 unit. c = 1.5 units. Therefore, angle a° is; atan(0.5/1)-atan(0.5/1.5) a = 26.5650511771-18.4349488229 a = 8.1301023542 °

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2389376

Let the radius of the red inscribed circle be r. Calculating r. 2a² = 6² a = √(18) a = 3√(2) units. 2b² = 8² b = √(32) b = 4√(2) units. c² = 6²+8² c = √(36+64) c = 10 units. 10² = 2d² d² = 50 d = √(50) d = 5√(2) units. d is the radius of the yellow ascribed semi circle. (5√(2))² = e²+(4√(2))² e² = 50-32 e = √(18) e = a = 3√(2) units. f = b-e f = 4√(2)-3√(2) f = √(2) units. f is length OD. g = d-r g = (5√(2)-r) units. h² = 2r² h = √(2)r units. It...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2385769

Calculating angle x. Let the two equal lengths of the ascribed square be 1 unit. tan10 = 1/a a = 5.6712818196 units. a is the square side considering the assume 1 unit. b = a-1-1 b = 5.6712818196-2 b = 3.6712818196 units. It implies; tanc = b/a tanc = 3.6712818196/5.6712818196 c = 32.9168410249° Therefore, the required angle x is; x = 10+c x = 10+32.9168410249 x = 42.9168410249°

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2384313

Let the side length of the three congruent regular hexagon be 1 unit. a = ⅙(180(6-2)) a = 120° a is the single interior angle of the three congruent regular hexagon. b² = 2-2cos120 b = √(3) units. tanc = 2√(3)/1 c = atan(2√(3)) c = 73.897886248° d = c-30 d = 73.897886248-30 d = 43.897886248° tan43.897886248 = e/√(3) e = ⅓(5) units. f² = (⅓(5))²+(√(3))² f = ⅓(2√(13)) units. f = 2.4037008503 units. g² = 1²+2/(2√(3))² g = √(13) units. g = 3.6055512755 units. h...

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