Mathematics Question and Solution
Notice.
Calculating the required angle, alpha.
4 units is the radius of the quarter circle.
It implies;
3² = 4²+4²-2*4*4cosa
9 = 32-32cosa
32cosa = 32-9
a = acos(23/32)
a = 44.0486256741°
b = ½(180-a)
b = 67.975687163°
c = 90-b
c = 22.024312837°
d² = 4²+2²-2*4*2cos22.024312837
d = 2.273236245 units.
It implies, the required angle, alpha is;
Let it be f.
(2.273236245/sin22.024312837) = (4/sine)
e = 41.2886037977
f = 180-e
f = 138.7113962023°
Again, f is the required angle, alpha.
