Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2402748

Calculating h, height of the ascribed right-angled triangle. Notice, 4 units is the radius of the inscribed circle. a² = h²+40² a= √(h²+1600) units. a is the hypotenuse of the ascribed right-angled triangle. Therefore; ½(4h)+½(4*40)+½(4*√(h²+1600)) = ½(40h) 4h+160+4√(h²+1600) = 40h 160+4√(h²+1600) = 36h 40+√(h²+1600) = 9h √(h²+1600) = 9h-40 h²+1600 = (9h-40)² h²+1600 = 81h²-720h+1600 80h²-720h = 0 80h² = 720h 8h = 72 h = 9 units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2402586

Calculating r, radius of the circle. 8² = 9²+7²-2*9*7cosa cosa = (9²+7²-8²)/(2*7*9) a = acos((9²+7²-8²)/(2*7*9)) a = 58.4118644948° (8/sin58.4118644948) = (9/sinb) b = 73.398450401° c = ½(180-a) c = ½(180-58.4118644948) c = 60.7940677526° d = ½(180-b) d = ½(180-73.398450401) d = 53.3007747995° tan60.7940677526 = r/e e = r/(tan60.7940677526) e = 0.5590169944r units. tan53.3007747995 = r/f f = r/(tan53.3007747995) f = 0.7453559925r units. Therefore, r, radius of the circle is; e+f = 7 0....

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2401648

Let the side length of the green square be x. Notice, radius of the two congruent circles is 5 units each. Therefore; a = (5-x) units. b = (5-½(x)) units. Observing Pythagoras Rule to get x, side length of the green square. 5² = b²+a² 5² = (5-½(x))²+(5-x)² 25 = 25-5x+(x²/4)+25-10x+x² 0 = 25-15x+(5x²/4) 5x²-60+100 = 0 x²-12x+20 = 0 Resolving the above quadratic equation via completing the square approach. (x-6)² = -20+(-6)² (x-6)² = 16 x = 6±√(16) x = 6±4 It...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2401460

Let BC be 1 unit. a = 180-57-49-33 a = 180-139 a = 41° a is angle BDC. Observing Sine Rule. (1/sin41) = (b/sin(49+33)) b = 1.5094191604 units. b is BD. c = 180-33-30-41 c = 180-104 c = 76° c is angle CAD. Observing Sine Rule. (1/sin41) = (d/sin57) d = 1.2783462019 units. d is CD. Observing Sine Rule. (1.2783462019/sin76) = (e/sin33) e = 0.7175515907 units. e is AD. Observing Cosine Rule. f² = 0.7175515907²+1.5094191604-2*0.7175515907*1.5094191604cos30 f = 0.9577402043 units. f is AB. Th...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2400085

Sir Mike Ambrose is the author of the question. Area Green exactly is; Area trapezoid with parallel sides 3 cm and (6-2√(3)) cm, and height (6-3√(3)) cm. = ½(6-3√(3))(3+(6-2√(3))) = ½(6-3√(3))(9-2√(3)) = ½(72-39√(3)) cm² = 3(24-13√(3))/2 cm²

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2400035

Let AB = 1 unit. Calculating CD. a = 180-40-60 a = 80° a is angle ADB. Observing Sine Rule. (1/sin80) = (b/sin40) b = 0.6527036447 units. b is AD. c = 180-80 c = 100° c is angle ADC. d = 180-100-30 d = 50° d is angle CAD. Therefore, Observing Sine. (0.6527036447/sin30) = (e/sin50) e = 1 unit. e is CD. It implies; AB = CD Proved!

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2399196

Calculating R, radius of the circle. 5² = (½(8))²+a² 25 = 16+a² a = √(25-16) a = 3 units. b = (R-3) units. Therefore, R is; R² = (R-3)²+(½(8))² R² = (R-3)²+4² R² = R²-6R+9+16 6R = 25 R = ⅙(25) units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2398894

Calculating R, radius of the ascribed circle. a² = 4.5²+2.9²-2*4.5*2.9cos60.8 a = 3.9908473908 units. (3.9908473908/sin60.8) = (4.5/sinb) b = 79.8304370724° c = ½(4.5) c = 2.25 units. Therefore, R, radius of the ascribed circle is; sin79.8304370724 = 2.25/R R = (2.25/sin79.8304370724) R = 2.2859127376 units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2398853

Calculating area red. tana = 3/5 a = atan(3/5)° b = 2a b = 2atan(3/5)° tanc = 5/3 c = atan(5/3)° d = 2c d = 2atan(5/3)° Therefore, red area is; 2(area circle with radius 5 units) - 4(area quarter circle with radius 5 units and angle 2atan(3/5)° - area triangle with height 5 units and base 5sin(2atan(3/5)) units) - 4(area quarter circle with radius 3 units and angle 2atan(5/3)° - area triangle with height 3 units and base 3sin(2atan(5/3)) units) = 2(5²π)-4(2atan(3/5)π*5²/360 - (0.5*5*5si...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2398565

Let a be the side of the inscribed square. 24² = a²+(2a)² 576 = a²+4a² 576 = 5a² a = √(576/5) a = 10.733126292 cm. b = ½(24-10.733126292) b = 6.633436854 cm. b = AM = DR. c = atan(6.633436854/(6+10.733126292)) c = 21.62463392714° c = Angle BPQ. tan21.62463392714 = d/10.733126292 d = 4.25488424946 cm. d = MQ. e = 0.5(10.733126292)+4.25488424946 e = 9.62144739546 cm. e = MO. f = 9.62144739546+12 f = 21.62144739546 cm. f = DM. g = atan(12/21.62144739546) g = 29.03047057929° g = Angle CMD...

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