A picture is always helpful:

Make a proportion with the correlating sides.

That should be: $\displaystyle \frac{x}{5.5} = \frac{2.7}{9}$

Solve for $\displaystyle x$.

As for the trigonometry part, that's kinda tough (unless I'm just missing something big).

I would use pythagorean theorem to find the missing side on the big triangle,

then use law of cosines to find the angle the ramp makes with the ground.

Then use Cosine Law in the smaller triangle.

There must be a simpler way, but I don't see it.