Mathematics Question and Solution
Let the radius of the inscribed yellow half circle be x.
Calculating x.
a = tan(3/4)°
a is angle ABC.
b = tan(4/3)°
b is angle BAC.
sin(atan(3/4)) = x/c
c = (5x/3)
c is OB.
sin(atan(3/4)) = x/d
d = (5x/4)
d is OA.
And AB is 5 units.
It implies;
OB+OA = 5
(5x/3)+(5x/4) = 5
20x+15x = 60
35x = 60
x = (60/35) units.
x = (12/7) units.
Notice, x is the radius of the inscribed yellow half circle.
Area inscribed yellow half circle is;
½(12/7)²π
= ½(144/49)π
= (72/49)π square units.
= 4.6162177767 square units.
