Are you talking about a literal compass and straightedge construction or do you just want the lengths of the legs of the right triangle?

Call the remaining two legs x and y.

Then we know that

and

<-- Since we have a right triangle.

Solving the first for y gives:

Inserting this into the second equation gives:

The quadratic formula says

or

So let x = 1.8834 cm, then y = 6.1166 cm. (Or x = 6.1166 cm and y = 1.8834 cm. Whichever.)

-Dan