Mathematics Question and Solution
Let the base of the triangle be 1 unit.
a = 20+100 = 120°
b = 10+10 = 20°
c = 190-a-b
c = 180-120-20
c = 40°
It implies;
(1/sin120) = (d/sin40)
d = 0.742227199 units.
e = 180-10-20
e = 180-30
e = 150°
It implies;
(0.742227199/sin150) = (f/sin20)
f = 0.5077133059 units.
g² = 0.5077133059²+1²-2*0.5077133059cos10
g = 0.507713306 units.
Therefore, the required angle, angle x is;
(0.507713306/sin10) = (0.507713306/sinx)
sin10 = sinx
It implies;
x = 10°
