Mathematics Question and Solution
Notice!
AB = AC
It implies, triangle ABC is isosceles.
a = 180-45-30
a = 105°
a is angle ADC.
b = ½(180-45)
b = ½(135)
b = 67.5°
b = angle ABC = angle ACB
c = 67.5-45
c = 22.5°
c is angle DBE.
d = 67.5-30
d = 37.5°
d is angle BCD.
Let BC be 1 unit.
Observing Sine Rule.
(1/sin(180-45-67.5)) = (e/sin67.5)
e = 1 unit.
e is BE.
Observing Sine Rule.
(f/sin(67.5-30)) = (1/sin(180-37.5-67.5))
f = 0.630236207 units.
f is BD.
Observing Cosine Rule.
g² = 0.630236207²+1²-2*0.630236207*1cos22.5
g = 0.4823619098 units.
g is DE.
Calculating the required angle x (angle BED).
Observing Sine Rule.
(0.4823619098/sin22.5) = (0.630236207/sinx)
sinx = 0.5
x = 30°
