Mathematics Question and Solution
Let the square side be 1 unit.
Let r be the radius of the semi circle.
Calculating r.
c² = 2(1)²
c = √(2) units.
c is the diagonal of the square.
tand = 1/0.5
d = atan(2)°
e = 180-d-45
e = (135-atan(2))°
sin(135-atan(2)) = r/f
f = r/sin(135-atan(2))
f = 1.0540925534r units.
(0.5/sin(135-atan(2))) = (g/sin(atan(2)))
g = 0.4714045208 units.
It implies;
r+f+g = c
r+1.0540925534r+0.4714045208 = √(2)
2.0540925534r = √(2)-0.4714045208
2.0540925534r = 0.9428090416
r = 0.4589905358 units.
Again, r is the radius of the semi circle.
Calculating a.
a² = 2r²
a² = 2(0.4589905358)²
a = √(0.4213446239)
a = 0.6491106407 units.
Therefore;
b = 1-a
b = 1-0.6491106407
b = 0.3508893593 units.
It implies;
a : b is;
0.6491106407÷0.3508893593
= 1.8499011826
= 1.85 to 2 decimal places.
