= Solution
The first peak is $001$, with $d_{001}=c$; the second is $110$, with $d_{110}=a/\sqrt2$. Applying <Bragg's law> with $\lambda=0.193604\,\mathrm{nm}$ gives
$$
\boxed{c=\frac\lambda{2\sin15.30^\circ}=0.3669\,\mathrm{nm},\qquad a=b=\frac\lambda{\sqrt2\sin20.24^\circ}=0.3957\,\mathrm{nm}.}
$$
Thus $c/a=0.927$, consistent with the approximate ratio used to order the reflections. These are the lengths of the supplied larger basal cell; the primitive basal <lattice parameter> is $a/\sqrt2=0.2798\,\mathrm{nm}$.
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