Mathematics Question and Solution
Calculating angle x.
Let BE be 1 unit.
a = 180-55-20
a = 105°
a is angle CBE.
b = a-30
b = 105-30
b = 75°
b is angle ABE.
(1/sin20) = (c/sin105)
c = 2.82417818114 units.
c is CE.
d = 180-55-15-75
d = 180-145
d = 35°
d is angle BAE.
(1/sin35) = (e/sin75)
e = 1.68404028665 units.
e is AE.
f² = c²+e²-2cecos15
f² = 2.82417818114²+1.68404028665²-2*2.82417818114*1.68404028665cos15
f = 1.27437435313 units.
f is AC.
It implies, angle x is;
(1.27437435313/sin15) = (1.68404028665/sinx)
sinx = 0.34202014332
x = asin(0.34202014332)
x = 20°
x is angle ACE.
