Answer:
BC = 4 cm
BE = 10.39
Step-by-step explanation:
ABCD is an isosceles trapezoid.
Measures of base angles of an isosceles trapezoid are equal.
[tex]\therefore m\angle ABC = m\angle DCB [/tex]
[tex]\because m\angle DCB = 120\degree [/tex]
[tex]\therefore m\angle ABC = 120\degree [/tex]
[tex] m\angle ABE = 120\degree-90\degree [/tex]
[tex] m\angle ABE = 30\degree [/tex]
in triangle ABE,
[tex]\cos 30\degree =\frac{BE}{12}[/tex]
[tex]\frac{\sqrt 3}{2} =\frac{BE}{12}[/tex]
[tex] BE = \frac{\sqrt 3\times 12}{2} [/tex]
[tex] BE =6\sqrt 3\: cm[/tex]
[tex] BE = 10.39 cm[/tex]
[tex]\sin 30\degree =\frac{AE}{12}[/tex]
[tex]\frac{1}{2} =\frac{AE}{12}[/tex]
[tex] AE = \frac{12}{2} [/tex]
[tex] AE =6 \: cm[/tex]
Next, Draw [tex] CF\perp AD [/tex]
FD = AE = 6
EF = 16 - (AE + FD) = 16 - (6+6) = 16-12
EF = 4 cm
BCFE is a rectangle.
Measures of the opposite sides of a rectangle are equal.
Therefore
BC = EF
BC = 4 cm
