How to determine directions of vectors of an electromagnetic wave

I did an exercise which probably is quite popular,
in which you draw an electromagnetic wave and prove that it should propagate at the speed of light $1 \over \sqrt {\mu_0\epsilon_0}$ using Farday's law and Ampere's law.

Basically if this is the wave:

Let's say the E-field (red) is in the X direction, the B-Field (blue) is in the Y direction, and the velocity of the wave is in the Z direction.

You take for example for ampere's law a surface in the ZY plane with a length L equal to the amplitude of the wave, and a width equal to $\lambda\over 4$ You do a similar thing with Faraday's law and you get the speed of light, assuming you know that the E-field and B-field propagate in this manner.

I got the right answer but I wondered about this: Let's say I only had the E-field and I know the wave propagates at the speed of light, I assume this is enough information to draw the B-field at each point.

But how will I know the direction? Both Faraday's law and Ampere's law say you need a closed loop integral and the rules I've been taught say you go over the loop in a clockwise direction for example and take the normal to the surface according to the right hand rule etc.

But clockwise and counter-clockwise direction don't really give me much information in this case, so how can I determine the direction of the B-field if I only have the E-field?

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Related question from OP: physics.stackexchange.com/q/20331/2451 –  Qmechanic Feb 14 '12 at 1:57

$$\mathbf{B} = \frac{1}{c}\hat{\mathbf{k}}\times\mathbf{E}$$
where $\hat{\mathbf{k}}$ is a unit vector that points in the direction of propagation of the wave. If you don't know which direction the wave is moving, you can't tell which way the magnetic field points.