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Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2798968

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Sir Mike Ambrose is the author of the question. Let the small inscribed circle's radius be x. x = 6 cm. Let the big inscribed circle's radius be y. y = 8 cm. Let the ascribed semi circle's radius be z.  = 18 cm. a² = 10²-8² a = 6 cm. b² = 12²-6² b = 6√(3) cm c = atan(z/b)° c = atan(18/6√(3))° c = atan√(3)° c = 60° d = atan(z/a)° d = atan(18/6) d = atan(3)° (a) Angle theta exactly is; Let it be e. e = 180-c-d e = 180-60-atan3 e = (120-atan3)° e = (atan(⅓)...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2798282

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a = ½(10) a = 5 units. a is the radius of the circle. b = (5-a) units. c = (5-2a) units. Calculating a. 5² = (5-2a)²+(5-a)² 25 = 25-20a+4a²+25-10a+a² 5a²-30a+25 = 0 a²-6a+5 = 0 a²-a-5a+5 = 0 a(a-1)-5(a-1) = 0 (a-5)(a-1) = 0 It implies; a ≠ 5 units. a = 1 unit. Recall. b = (5-a) units. And a = 1 unit. b = 4 units. c = (5-2a) units. And a = 1 unit. c = 3 units. Therefore, the length of the square is; Let it be d. d = 2c+2a And c = 3 units, a = 1 uni...

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...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2797386

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Notice; a² = 5² - (⅕(√(481)))² a = ⅕(12) units. b = 5-a b = ⅕(13) units. c² = 4²-(⅕(12))² c = ⅕(16) units. d = atan(4/3)° (a) Area A exactly is; ½*⅕(16)*(5+⅕(13)) - atan(4/3)π*16/360 = ((8*38)/25) - (2atan(4/3)π/45) = (304/25) - ((2atan(4/3)π)/45) = (2736-10πatan(4/3))/225 square units. = 4.74163825599 square units. (b) Calculating Area B to 2 decimal places. ½*10(10+5) - ½*⅕(16)(5+⅕(13)) - ((atan½+ata¾)π*16/360) - (⅕(13)*⅕(34-√(481))) - ½*⅕(√(481))(5+⅕(13)) - ((atan(12/√(481))+(2tan2-...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2797369

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Calculating x. (2√(3)/sin100) = (a/sin60) a = 3.0462798357 units. b = 180-(180-100-60) b = 160° Therefore, the required length, x is; x² = 2(3.0462798357)²-2(3.0462798357)²cos160  x = 6 units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2796126

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Calculating area of the inscribed triangle. a = 2r a = 2√(5) units. a is the side length of the ascribed square. tanb = √(5)/(2√(5)) b = atan(½)° c = 2b c = 2atan(½)° d = 90-2atan(½) d = 90-atan(½)-atan(½)° d = (atan(2)-atan(½))° Therefore, area inscribed triangle is; 0.5*2√(5)*2√(5)sin(atan(2)-atan(½)) = 10*0.6 = 6 square units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2795785

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Sir Mike Ambrose is the author of the question. Let the side of the square be 2 units. Area square is; 2² = 4 square units. Area orange is; Area triangle with two side 0.70710678119 units and 1.2928932188 units, and angle (90+asin(⅓))° + Area triangle with two side 1.66764761969 units and 1.20710678117 units, and angle 66.436529825° = 0.5*0.70710678119*1.2928932188sin(90+asn(⅓)) + 0.5*1.66764761969*1.20710678117sin(66.436529825) = 0.43096440627 + 0.9225889843 = 1.3535533905...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2795727

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Sir Mike Ambrose is the author of the question. Area red is; Area triangle with two side 4 cm and 8 cm, and angle 110°. = 0.5*4*8sin110 = 15.0350819326 cm² Area blue is; Area triangle with height 4.47952822702 cm and base (4.47952822702tan33.67018696) cm = 0.5*4.47952822702*4.47952822702tan33.67018696 = 6.6836970062 cm² Therefore; Area Blue + Area Red in cm² to 2 d. p. is; 6.6836970062 + 15.0350819326 = 21.7187789388 cm² ≈ 21.72 cm²

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2795137

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a² = 2²+2²-2*2*2cos120 a = √(8+½(8)) a = √(12) a = 2√(3) units. a is the side length of each of the 4 inscribed small regular hexagon. sin30 = b/a b = asin30 b = ½*2√(3) b = √(3) units. c = 4b+3a c = 4(√(3))+3(2√(3)) c = 4√(3)+6√(3) c = 10√(3) units. c is the height of the big ascribed regular hexagon. d = ½(c) d = 5√(3) units. sin60 = d/e ½√(3)e = 5√(3) e = 10 units. e is the side length of the big ascribed regular hexagon. f² = 2(2√(3))²-2(2√(3))²cos120 f = 6...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2794675

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Let a be the congruent side lengths each. b = ½(2) b = 1 unit. c²+1² = a² c = √(a²-1) units. d = ½(180-45) d = ½(135) d = 67.5° tan67.5 = e/1 e = 2.4142135624 units. e = (1+√(2)) units. f = 1+e f = (2+√(2)) units. f is the radius of the ascribed quarter circle. g = f-2 g = √(2) units. Therefore, blue area is; ½*(fg) = ½*(2+√(2))*√(2) = ½(2+2√(2)) = (1+√(2)) square units. = 2.4142135624 square units.
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