Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2003758

Let the inscribed regular hexagon side length be 1 unit. a² = 2-2cos120 a = √(3) units. sin30 = b/1 b = ½ units. c = 1+b c = (3/2) units Calculating r, radius of the ascribed quarter circle. r² = (3/2)²+√(3)² r² = (9/4)+3 r = √(21/4) r = ½√(21) units. Area quarter circle is; ¼(½√(21))²π = (21π/16) square units. = 4.12334035784 square units. Calculating the shade area. tand = √(3)/(3/2) d = atan(2√(3)/3)° e = 90-d e = (90-atan(2√(3)/3)))° f² = √(3)²+(½)...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2000816

Let the side of the regular pentagon be 2 units. cos36 = a/2 a = 1.61803398875 units. Where a is the radius of the semi circle. Area semi-circle is; ½(1.61803398875)²π = 4.11239817295 square units. Calculating area S. b = 108-36 b = 72° c = 1.61803398875-1 c = 0.61803398875 units. tan72 = d/0.61803398875 d = 1.90211303259 units. e = atan(1.90211303259)° e = 62.26769855229° (f/sin62.26769855229) = (1.61803398875/sin(180-36-62.26769855229) f = 1.4472135955 units. Area S is; (108π*1....

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Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/1999856

Let the height of the yellow area trapezoid be a. Calculating a. tan72 = a/b b = (a/tan72) cm. c = 2b c = (2a/tan72) cm. d = 8+c d = (8+(2a/tan72)) cm. It implies; ½*a(8+(8+(2a/tan72))) = 56.23 a(16+0.64983939247a) = 112.46 0.64983939247a²+16a- 112.46 = 0 Therefore; a = 5.70627 cm. d = (8+(2a/tan72)) d = 11.70815903005 cm. tan18 = e/5.70627 e = 1.85407951502 cm. f = 2e f = 3.70815903005 cm. (g/sin36) = (8/sin108) g = 4.94427191 cm. sin72 = h/8 h = 7.60845213036 cm. i = h-a i =...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/1999278

Considering similar triangles ADC and CDB ratios. Let CD be a. 16 = a a = 4 Cross Multiply. a² = 64 a = 8 units c² = 16²+8² c = 8√(5) units. c = AC. Calculating r1. 16r1+8r1+8√(5)r1 = (16*8) r1(24+8√(5)) = 128 r1 = 128/(24+8√(5)) r1 = 16/(3+√(5)) r1 = (12-4√(5)) units. d² = 8²+4² d = 4√(5) units. d is BC. Calculating r2. 4r2+8r2+4√(5)r2 = (8*4) r2(12+4√(5)) = 32 r2(3+√(5)) = 8 r2 = 8/(3+√(5)) r2 = (6-2√(5)) units. Calculating EF. (EF)² = (r1+r2)²+(r1-r2)² (EF)² = ((12-4√(5))+(6-2√...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/1997920

Calculating a. (1/sin120) = (a/sin20) a = 0.39493084363 units. Calculating b. (1/sin120) = (b/sin40) b = 0.74222719897 units. Therefore, observing the proof; (1/a)+(1/b) = 3ab+3 (1/a)+(1/b) is; 1/0.39493084363+1/0.74222719897 = 3.8793852416 3ab+3 is; 3*0.39493084363*0.74222719897+3 = 3.87938524156 Proved.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/1997583

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))+(2t...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/1997564

Let AB be 1 unit. BC = 3 units. It implies; AC = 1+3 AC = 4 units. AC is a side length of the square. Radius of the inscribed half circle a is; ½(BC) a = ½(3) units. a = 1.5 units. b = 1.5+AB b = 1.5+1 b = 2.5 units. b = ½(5) units. c²+(1.5)² = (2.5)² c² = 2.5²-1.5² c = 2 units. Considering similar triangle ratios. 2 = 4 1.5 = d Cross Multiply. d = 3 units. tane = (3/4) e = atan(3/4)° f = atan(4/3)° Calculating g, side length of the regular triangle. (4/sin120) = (g/sin(atan(4/3)))...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/1996975

Let a be 1 unit. (1/sin48) = (b/sin24) b = 0.54731813925 units. (1/sin48) = (c/sin108) c = 1.27977277603 units. DC = 1.27977277603+0.54731813925+1 DC = 2.82709091528 units. Therefore, the required angle x is; (2.82709091528/sin36) = (1/sinx) x = 12°

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/1996244

Let the radius R, of the half circle be 1 unit. sin30 = c/1 c = ½ units. c = 0.5 units. cos30 = d/1 d = ½√(3) units. d = 0.86602540378 units. e = 1-0.86602540378 e = 0.13397459622 units. f² = (0.13397459622)²+(0.5)² f = 0.51763809021 units. Calculating r, radius of the small inscribed yellow circle. Considering similar triangle ratios. 0.51763809021 = (1-r) 0.5 = (0.5+r) Cross Multiply. 0.5-0.5r = 0.51763809021r+0.2588190451 0.5-0.2588190451 = 0.5r+0.51763809...

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