Mathematics Question and Solution
Let the radius of the quarter circle be a.
b = 2a units.
c = 4+5
c = 9 units.
It implies;
3²+9² = (2a)²
4a² = 90
a² = ½(45)
a = ½(3√(10)) units.
a = 4.7434164903 units.
Again, a is the radius of the quarter circle.
d² = 5²-(½(3√(10)))²
d² = 25-½(45)
d = √(½(5))
d = ½√(10) units.
e = a-d
e = ½(3√(10))-½√(10)
e = √(10) units.
f = 180-atan(3)-atan(3/4)
f = 71.5650511771°
It implies;
The required length, x is;
x² = 4²+10-2*4√(10)cos71.5650511771
x = 4.2426406871 units.
