Mathematics Question and Solution
Calculating AB, the side length of the ascribed square.
Let AB be a.
It implies;
a²+a² = 8²
2a² = 64
a² = 32
a = 4√(2) units.
Again a is AB, the side length of the ascribed square.
Therefore, r, radius of the inscribed half circle is;
r = ½(a)
r = ½(4√(2))
r = 2√(2) units.
tanb = a/r
tanb = ((4√(2))/(2√(2)))
tanb = 2
b = atan(2)°
c = 2b
c = 2atan(2)°
d = 180-c
d = (180-2atan(2))°
e = ½(d)
e = 0.5(180-2atan(2))°
Calculating x.
Notice; x = AE = EP
It implies;
tan(0.5(180-2atan(2))) = x/r
tan(0.5(180-2atan(2))) = x/(2√(2))
x = 2√(2)tan(0.5(180-2atan(2)))
x = √(2) units.
x = 1.4142135624 units.
