Mathematics Question and Solution
a = 180-60-40
a = 80°
(6/sin80) = (b/sin40)
b = 3.916221868 units.
(6/sin80) = (c/sin60)
c = 5.2763114494 units.
Calculating r, radius of the inscribed circle.
5.2763114494r+3.916221868r+6r = 3.916221868*6sin60
15.1925333174r = 20.3492857473
r = 1.3394267646 units.
Calculating d, radius of the ascribed circle.
e = ½(80-2*80)
e = ½(20)
e = 10°
Therefore;
cos10 = 3/d
d = 3/cos10
d = 3.0462798357 units.
tan40 = 1.3394267646/f
f = 1.5962666587 units.
Area Blue is;
Area sector with radius 3.0462798357 units and angle 80° - Area triangle with height 3.0462798357 units and base 3.0462798357sin80 units + 2(area triangle with height 1.5962666587 units and base 1.3394267646 units - angle sector with radius 1.3394267646 units and angle 50°)
= 80π*3.0462798357²/360-0.5*3.0462798357²sin80+2(0.5*1.5962666587*1.3394267646-50π*1.3394267646²/360)
= 6.4785371043-4.5694197536+2(1.0690411431-0.78280812)
= 2.4815833969 square units.
