Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2026802

Let the side length of the regular hexagon be 1 unit. sin60 = a/1 a = ½√(3) units. tanb = (a/1) b = atan(0.5√(3))° b = 40.89339464913° b is angle DEH. c = atan(2/√(3)) c = 49.10660535087° d = 120-40.89339464913 d = 79.10660535087° e = 40.89339464913-30 e = 10.89339464913° It implies, the required angle, angle EIH is; d+e = 79.10660535087+10.89339464913 = 90°

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2026658

Let r be the radius of the inscribed circle. Calculating r. a = √(2*24²) a = 24√(2) units. b = √(2*r²) b = √(2)r units. It implies; 16+r+√(2)r = 24√(2) r(√(2)+1) = (24√(2)-16) r = (24√(2)-16)/(√(2)+1) r = 8(8-5√(2)) units. r = 7.43145750508 units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2025221

Sir Mike Ambrose is the author of the question. Let the side length of the inscribed regular hexagon be 1 unit. Calculating r, radius of the circle. 1+2(sin30) r = 2 units. Area circle is; π(2)² = 4π square units. = 12.56637061436 square units. a = (1800/12) a = 150° b² = 2-2cos150 b = 1.93185165258 units. 2² = c²+1.93185165258²-2*1.93185165258*ccos135 4 = c²+3.73205080758+ 2.73205080757c c²+2.73205080757c-0.26794919242 = 0 c = 0.0947876 unit. (2/sin135) = (1.93185165258/sind) d = 43.0...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2024003

Sir Mike Ambrose is the author of the question. sin30 = a/12 a = 6 cm. sin60 = b/12 b = 6√(3) cm. Let the inscribed square side be c. Calculating c. (c/sin60)+(csin30) = 6 (⅓(2√(3))+½)c = 6 ⅙(4√(3)+3)c = 6 c = 36/(4√(3)+3) cm. (a) Area Blue exactly is; c² = (36/(4√(3)+3))² = 1296/(4√(3)+3)² = 1296/(48+24√(3)+9) = 1296/(57+24√(3)) = 432/(19+8√(3)) = 432(19-8√(3))/169 cm². (b) Calculating Shaded area to 2 decimal places. Notice; Blue square side is; 3.62603375102 cm. tan60 = c/...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2023937

Let angle BAC = 30° Let AB = AC = 1 unit. a² = 2-2cos30 a = 0.51763809021 units. a is BC. Since; BK = 2CK, therefore; 3CK = BC CK = 0.51763809021/3 CK = 0.17254603007 units. It implies; BK = 2*0.17254603007 BK = 0.34509206014 units. b² = 1+0.34509206014²-2*0.34509206014cos(0.5(180-30)) b = 0.96977097039 units. b is AK. (0.96977097039/sin75) = (1/sinc) c = 84.89609063879° c is angle AKB. d = 180-84.89609063879-30 d = 65.10390936121° d is angle PBK. (e/sin65....

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2023843

Let the two congruent square side be 1 unit. a = √(2) units a is a diagonal of one of the congruent squares. tanb = 1/(√(2)+1) b = 22.5° c = 90-b c = 67.5° d = ½(180-135) d = ½(45) d = 22.5° e = 180-67.5 e = 112.5 f = 180-112.5-22.5 f = 45° It implies, the required angle alpha is; 180-45 = 135°

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2023727

Calculating a, side length of the regular hexagon. Notice; Red Area is 122 square units. sin30 = b/a b = (a/2) units. c = a+2b c = 2a units. sin60 = d/a d = (√(3)a/2) units. It implies; 122+0.5*2a*(2a/3)sin60 = 0.5(a+2a)(√(3)a/2) 122+⅓(√(3)a²) = ¼(3√(3))a² 122 = ¼(3√(3))a²-⅓(√(3)a²) 122 = (5√(3)a²)/12 1464 = 5√(3)a² a² = 1464/(5√(3)) a = √(169.04815881872) a = 13.00185213032 units. ≈ 13 units to the nearest whole number.

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Our certified, experienced, resilient, productive and committed Math Educators will be glad to be at your service. We make teaching and learning Mathematics fun for learners, we expose the simplicity and beauty of Mathematics to our learners, and mentor them to appreciate and love Mathematics. Communicate us to mentor/educate you Mathematics better online at affordable tuition. We are smart and clever.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2022408

Let AB be 2 units. Therefore; BC = 1 unit. tan30 = a/3 a = √(3) units. tan30 = b/1 b = ⅓(√(3)) units. c = a-b c = ⅔(√(3)) units. d² = (⅓√(3))²+1² d = ⅔(√(3)) units. sin60 = ⅔*√(3)/e e = ⅓(4) units. sin30 = f/⅔(√(3)) f = ⅓(√(3)) units. sin60 = g/⅔(√(3)) g = 1 unit. h = e-g h = ⅓ unit. tani = (⅔*√(3))/(⅓(4)) i = atan(√(3)/2)° tan(atan(√(3)/2)) = j/(⅓) j = ⅙(√(3)) unit. l = j+b = ½(√(3)) unit. Therefore; Area Yellow is; ½*1(⅙(√(3))+⅔(√(3))) = ½*⅙(5√(3)) = 5√(3)/12 square units....

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2020152

Let AB be 1 unit. Therefore; BC = 2 units. It implies, the regular hexagon side length is 3 units. a = 120-108 a = 12° b² = 2²+3²-2*2*3cos12 b = 1.1234895599 units. (1.1234895599/sin12) = (2/sinc) c = 21.72287686377° d = 120-c d = 120-21.72287686377 d = 98.27712313623° Calculating Length Blue. Let it be e. e² = 3²+1.1234895599²-2*3*1.1234895599cos98.27712313623 e = 3.35151630086 units. f = 180-12-21.72287686377 f = 146.27712313623° (3.35151630086/sin98.27712313623) = (3/sing) g = 62...

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