Reciprocal Lattices and Ewald Sphere: Solving for a* and c* in a Tetragonal Cell

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PhysicsKid99
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Homework Statement


I have to draw a reciprocal lattice of a tetragonal cell with parameters a=3A and c=5A, a body-centred lattice. How do I find a* and c*? I also have to draw an Ewald sphere, and lamda=1.5. However, if I use my solutions (I think they're wrong, see below) I get something that is impossible to draw because the scale is huge.

Homework Equations


Radius of E sphere= 1/lamda

The Attempt at a Solution


a*=1/9 and c*= 1/25, the radius= 2/3
 
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Not an area I know anything about, but from a little reading it seems the reciprocal lattice will be a face-centred tetragonal lattice, yes?
The parameters are obtained by dividing vector cross products by the scalar triple product.
Please post your working for your attempted solution. (I get a different answer.)