Mathematics Question and Solution
a = 180-100-50
a = 30°
(20/sin100) = (b/sin30)
b = 10.1542661189 cm
c = ½(180-100)
c = 40°
Let d be the radius of the circle.
tan40 = d/e
e = 1.1917535926d .
f = (10.1542661189-1.1917535926d) units.
g = 180-50
g = 130°
sin(0.5*130) = d/h
h = 1.103377919d cm.
Calculating d.
cos(0.5*130) = (10.1542661189-1.1917535926d)/1.103377919d
10.1542661189-1.1917535926d = 0.4663076582d
1.6580612508d = 10.1542661189
d = 10.1542661189/1.6580612508
d = 6.1241803427 cm.
Again, d is the radius of the circle.
Recall.
e = 1.1917535926d
And d = 6.1241803427 cm.
e = 1.1917535926*6.1241803427
e = 7.2985139251 cm.
Shaded Area in cm square units is;
2(area triangle with height 7.2985139251 and base 6.1241803427 cm - area sector with radius 6.1241803427 cm and angle (0.5(180-80))°
= 2((0.5*7.2985139251*6.1241803427)-(50π*6.1241803427*6.1241803427÷360))
= 2(22.3487077556-16.3648985967)
= 2*5.9838091589
= 11.9676183179 cm²
≈ 12 cm²
