Answer:
12.7cm
Step-by-step explanation:
there are 2 triangles , triangle ABC and triangle BCD
use Pythagoras theorem for triangle ABC to find the line BC
let BC = h
12^2=6^2+h^2
making h the subject
h=
[tex] \sqrt{ {12}^{2} - {6}^{2} } \\ [/tex]
h =
[tex]6 \sqrt{3} [/tex]
so line BC is
[tex]6 \sqrt{3} [/tex]
for triangle BCD, there's an angle 55 degrees
sin theta = opposite/hypotenuse
where BC is the opposite
theta which is the angle = 55
[tex]h = \frac{6 \sqrt{3} }{sin55} [/tex]
[tex]sin55 = \frac{6 \sqrt{3} }{h} [/tex]
[tex]h = 12.69[/tex]
note h = CD
in 3 s.f ,h= 12.7cm
