Mathematics Question and Solution

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

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/2922210

Area of coloured region is; Area triangle with height 53.3479501083 m and base 60sin(102.042575143) m + Area triangle with height 100.027406452 m and base √(5924)sin(12.5245961777) m = (½*53.3479501083*60sin(102.042575143)) + (½*100.027406452*√(5924)sin(12.5245961777)) = 1565.21739131 + 834.782608691 = 2400 m²

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2893310

Let a be the diameter of the semi circle. a² = b²+14² b² = a²-196 b = √(a²-196) It implies; b² = 6²+6²-2*6*6(-cosc) a²-196 = 72+72cosc a²-196-72 = 72cosc 72cosc = a²-268 cosc = (a²-268)/72 --- (1). cosc = 14/a --- (2). Equating (1) and (2). cosc = cosc (a²-268)/72 = 14/a a³-268a = 1008 a³-268a-1008 = 0 Resolving the polynomial equation. a = 18 units. It implies; Radius, r of the semi circle is; ½(a) = ½(18) = 9 units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2876028

Let the side of the regular pentagon be 1 unit. a² = 2-2cos108 a = 1.61803398875 units. sin30 = b/0.5 b = 0.25 unit. c = 2b c = 0.5 unit. Where c is the inscribed square side. Area Square is; (0.5)² = 0.25 square units. Inscribed circle radius d is; d = ½(b) d = 0.125 unit. e = 0.5-0.125 e = 0.375 unit. f = 2atan(0.125/0.375) f = 36.86989764584° tan36.86989764584 = g/0.5 g = 0.375 unit. Shaded Area is; 0.5*0.375*0.5-π*0.125*0.125 = 0.0446626...

Mathematics Question and Solution

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

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/2864071

Let the two equal inscribed right-angled triangle side lengths be a each. Calculating a. 0.5a² = 50 a² = 100 a = 10 units. a is EU. Notice! Arc TU = Arc US. Let b be the radius of the ascribed quarter circle. Calculating b. sin(0.5*45) = (0.5*10)/b sin22.5 = 5/b b = 5/sin(22.5) b = 13.0656296488 units. Therefore, ascribed quarter circle perimeter is; ¼*2πb+2b = 0.25*2*π*13.0656296488+2*13.0656296488 = 46.6547023572 units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2837750

Area blue is; Quarter the area of the square. = ¼(10)² = ¼(100) = 25 cm²

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2834872

Calculating r, radius of the circle. (r/tan40)+(r/tan30) = 10 r = 3.42020143326 cm. (a/sin60) = (10/sin40) a = 13.47296355334 cm. tan40 = 3.42020143326/b b = 4.07603734548 (4.07603734548/sin50) = (c/sin80) c = 5.24005260459 cm. d = 13.47296355334-4.07603734548 d = 9.39692620786 cm. e² = 9.39692620786²+5.24005260459²-2*9.39692620786*5.24005260459cos130 e = 13.38142726359 cm. (13.38142726359/sin130) = (5.24005260459/sinf) f = 17.45618925878° g = 100-17.4561892587...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2833435

Notice; AB = 25 units. cos30 = 8√(3)/a a = 16 units. tan30 = b/(8√(3)) b = 8 units. Let the side of the regular hexagon be c. c = ¼(AC) Calculating AC. ((AC)/sin46) = (25/sin74) AC = 18.70821971213 units. c = ¼(18.70821971213) c = 4.67705492803 units. Calculating r, radius of the circle. (r/sin16) = (25/sin148) r = 13.00374294827 units. Calculating Shaded Area. cos30 = d/4.67705492803 d = 4.05044838257 units. e = 2d e = 8.10089676514 units. tan16...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2825213

a² = R²+6² a = √(R²+36) units. a is OB. b = a-4 b = (√(R²+36)-4) units. c = 6+4 c = 10 units. It implies; 10² = R²+(√(R²+36)-4)² 100 = R²+R²+36-8√(R²+36)+16 48 = 2R²-8√(R²+36) 8√(R²+36) = 2R²-48 4√(R²+36) = R²-24 16(R²+36) = R⁴-48R²+576 16R²+576 = R⁴-48R²+576 16R² = R⁴-48R² R² = 64 R = 8 units.

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