Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/1948278

Let the congruent lengths be 1 unit. (1/sin50) = (a/sin80) a = 1.28557521937 units. sin(60) = b/2 b = √(3) units. b = 1.73205080757 units. c = 20° d² = 1.73205080757²+1.28557521937²-2*1.73205080757*1.28557521937cos20 d = 0.68404028665 units. Therefore, the required angle is; Let it be e. (0.68404028665/sin20) = (1.28557521937/sine) e = 40°

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/1948081

Let the square side length be 1 unit. Therefore, the regular hexagon side length is 1 unit as well. sin30 = a/1 a = 0.5 units. b = 1+a b = 1+0.5 b = 1.5 units. cos30 = c/1 c = ½√(3) units. d = 1+c d = 1+½√(3) d = ½(2+√(3)) units. e = 3+c e = 3+½√(3) e = ½(6+√(3)) units. Therefore; angle ABC is; atan(d/b) + atan(e/b) = atan(½(2+√(3))/1.5) + atan(½(6+√(3))/1.5) = 51.206023113+68.793976887 = 120°

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/1946655

Let the height and base of area triangle C be 2 units and 3 units respectively. Therefore; Area Triangle C is; ½*2*3 = 3 square units. tana = (2/3) a = atan(2/3)° b = 189-a b = 180-atan(2/3) b = 146.30993247402° c = ½(180-146.30993247402) c = 16.84503376299° Let the radius of the big circle be d. Calculating d. e = ½(146.30993247402) e = 73.15496623701° f = (3-d) units. tan73.15496623701 = d/(3-d) d = 9.9083269132-3.30277563773d 4.30277563773d = 9.9083269132 d = 9.9083269132/4.3027...

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Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/1945925

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 units. h = f-g h = 0.5005810...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/1945920

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 = 0.04466261479 square units. (a) Area Shaded ÷...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/1945276

Let the radius of the circle be a. a² = 2²+4² a² = 20 a = 2√(5) cm. Area Blue is; Area half circle with radius 2√(5) cm - Area red rectangle with length and base 6 cm and 2 cm respectively. = ½(2√(5))²π - (6*2) = 10π-12 = 2(5π-6) cm² = 19.4159265359 cm²

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/1945219

Let the four congruent lengths be 1 unit each. a² = 2-2cos38 a = 0.65113630891 units. b = ½(180-38) b = 71° c = 60+71 c = 131° d² = 0.65113630891²+1²-2*0.65113630891cos131 d = 1.50941916044 units. Therefore; The required angle x is; (1/sinx) = (1.50941916044/sin131) x = 30°

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/1945064

Let a be the radius of the inscribed half circle. tanb = (3/4) b = atan(3/4)° tan(atan(3/4)) = a/(4-a) (3/4) = a/(4-a) 4a = 12-3a 7a = 12 a = (12/7) units. c² = 3²+4² c = √(25) c = 5 units. sin(atan(3/4)) = (12/7)/d (3/5) = (12/7)/d 3d = (60/7) d = (20/7) units. Calculating x. x = c-d-a x = 5-(20/7)-(12/7) x = 5-(32/7) x = ⅐(35-32) x = (3/7) unit.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/1944808

a = 360-140-80 a = 140° cos20 = 1/b b = 1.06417777248 units. (1.06417777248/sin30) = (c/sin70) c = 2 units. d² = 4+1.064177772482²-4*1.06417777248cos140 d = 2.89711998506 units. (2.89711998506/sin140) = (2/sine) e = 26.34291130662° f = 40-e f = 13.65708869338° g = 20+26.34291130662 g = 46.34291130662° tan46.34291130662 = h/2 h = 2.09602104183 units. Area ABC is; 0.5*2*2.09602104183 = 2.09602104183 square units. Calculating Area Blue. i = 60-26.34291130662 i = 33.65708869338= (1....

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