This question is quite similar to the one earlier, so we will be using SOH CAH TOA again.
We first have to calculate the length of CB. All we have to do for this is use Pythagoras's theorem.
√12² - 6²
= 10.39230... cm
Now we use SOH CAH TOA for the next part.
Lets label the sides.
CB is the opposite
CD is the hypotenuse
We will use sin, since we know the angle, the opposite and we want to know the hypotenuse.
sin(55) = opp / hyp
sin(55) = 10.39230... / x
10.39230.. / sin(35) = x (you re-arrange the equation to get x alone)
12..68666.. = x
So x = 12.687 to 3 significant figures