Mathematics Question and Solution
Let the diameter of the inscribed half circle be 2 units.
It radius is 1 unit.
Calculating x, angle alpha.
tana = 1/0.5
a = atan(2)°
b = 2a
b = 2atan(2)°
c = 180-b
c = (180-2atan(2))°
d² = 2(0.5)²-2(0.5)²cos(180-2atan(2))
d = 0.4472135955 units.
e = ½(180-(180-2atan(2)))
e = ½(2atan(2))°
e = atan(2)°
f = 90-e
f = atan(½)°
It implies;
g² = 0.4472135955²+2²-2*2*0.4472135955cos(atan(½))
g = 1.6124515497 units.
(1.6124515497/sin(atan(0.5))) = (0.4472135955/sinh)
h = 7.1250163489°
Therefore, x, the required angle alpha is;
x+h = atan(1/2)
x = atan(1/2)-h
x = atan(0.5)-7.1250163489
x = 19.4400348282°
Again, x is the required angle alpha.
It implies;
tanx is;
tan(19.4400348282)
= 0.3529411765
