a² = 3²+4²
a = 5 cm.
Where a is AC.
b = atan(4/3)°
Where b is angle DAC.
c = 60+atan(4/3)
c = 113.13010235416°
Where c is angle EAC.
d² = 3²+5²-2*3*5cos113.13010235416
d = 6.76643256752 cm.
Where...
The radius of the circle is 6 cm.
a = atan(2)°
Where a is angle AOB = angle COE.
Angle BOE = 180-atan(2)
= 116.56505117708°
Angle OBE = ½(180-116.56505117708)
= 31.71747441146°
b =...
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Let r = 1 units.
Let the ascribed half circle's radius be x.
Therefore;
a = (x-2) units.
b = ½(x-2) units.
c = x-b
c = x-½(x-2)
c = ½(x+2) units.
d = 2a
d = 2(x-2)
d = (2x-4) units.
Therefore...
Let the side length of square ABCD be a.
Area Square ABCD will be a²
Calculating a²
Notice, he three inscribed plane shapes, two congruent right-angled triangle and a parallelogram has equal area....
Let the regular pentagon side be 1 unit.
a = ⅕(180*3)
a = 108°
a is an angle of the regular pentagon.
b = 108-36
b = 72°
c = 180-45-72
c = 180-117
c = 63°
(d/sin63) = (1/sin45)
d = 1.26007351067...
Let the inscribed regular pentagon side be 1 unit.
Area small/inscribed pentagon is;
0.5*5(1/(2tan(180/5)))
= 1.72047740059 square units.
Calculating Shaded Area.
a² = 2-2cos(60+108)
a = 1.989043...
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Let BD be 1 unit.
Therefore;
DC = 2 units.
a = 180-60
a = 120°
b = 180-120-45
b = 15°
(1/sin15) = (c/sin120)
c = 3.34606521495 units.
d² = 3.34606521495²+3²-2*3.34606521495*3cos45
d = 2.449489...
a² = 2*12²
a = 12√(2) cm.
Where a is AC = CF.
b = 90+45
b = 135°
Where b is angle BCE.
c² = (12√(2))²+12²-24*12√(2)cos135
c = 12√(5) cm.
Where c is BE.
(12√(5)/sin135) = (12/sind)
d = 18.43494882...
