X-rays diffraction in a solid, Bragg's law

[fluidistic]

Homework Statement

The X-rays diffraction diagramm of a cubic crystal shows lines for the following angles 2 \delta = 31.47º, 39.74º, 47.58º, 64.71º and 77.59º when the X-rays have a wavelength of 1.54 \times 10 ^{-10}m.
Determine the crystal stucture of the net, the Miller indices of the diffractive planes and the parameter of the net.

Homework Equations

\left ( \frac{\lambda }{2a } \right )^2 =\frac{sin ^2 (\theta )}{h^2+k^2+l^2} where h, k and l are Miller indices.

The Attempt at a Solution

First I am not sure what they mean by "2 delta's". Second, it's the first time I'm asked to solve such an exercise and I've thought on it and I don't see a direct way to solve the problem, because I don't know the "parameter of the net", which I guess is "a" in the formula, nor do I know h, k and l.
So I've started a try. I've tested for a bcc crystal structure and the test resulted in a negative answer. Please tell me if my approach is correct.
I considered the angle \theta = 31.47º. From the given formula, I get a = \frac{\lambda }{\sin \left ( \frac{31.47}{2} \right ) } \approx 5.68 \times 10 ^{-10}m. I considered h=2, k=l=0 because in a bcc crystal, h+k+l must be even.
I then tried h=k=2 and l=0 and I took the value of "a" I just obtained in order to see if I could find an angle close to 39.74º but I reached a value for theta of about 22.55º.
I realize that there are infinitely many other possibilities for the values of h, k and l for a bcc crystal structure so that I can't really affirm that the crystal isn't bcc. So how do I solve the problem? Should I work out a lot of possible values for h, k and l?

 

[member 553083]

Is there a way to find the correct values of h, k and l without trying all possibilities? Thank you very much in advance.