Mathematics Question and Solution
Let the three equal inscribed lengths be y.
a = 5+4
a = 9 units.
a is the radius of the ascribed half circle.
b² = y²+y²
b = √(2)y units.
Notice.
a = b
√(2)y = 9
y = ½(9√(2)) units.
c = 2y
c = 2*½(9√(2))
c = 9√(2) units.
It implies;
9² = 5²+(9√(2))²-2*5*9√(2)cosd
81 = 187-90√(2)cosd
90√(2)cosd = 106
d = acos(106/(90√(2)))°
d = 33.6110339926°
Therefore, the required length, x is;
sind = x/(9√(2))
x = 9√(2)sin33.6110339926
x = 7.04556598153 units.
