Mathematics Question and Solution
Calculating the required angle, alpha.
Let it be a.
Let R = 2 units, radius of the ascribed semi circle.
b = (2-r) units.
It implies;
Calculating r.
(2-r)² = 2r²
2-r = √(2r²)
2-r = √(2)r
2 = √(2)r+r
(1+√(2))r = 2
r = 2/(1+√(2))
r = 2(1-√(2))/(-1)
r = 2(√(2)-1) units.
r = 0.8284271247 units.
r is the radius of the inscribed circle.
c = 2+r
c = 2+0.8284271247
c = 2.8284271247 units.
Therefore, the required angle, alpha (a) is;
tana = r/c
tana = 0.8284271247/2.8284271247
a = atan(0.8284271247/2.8284271247)
a = 16.3249499363°
a ≈ 16.325° to 3 decimal places.
