From this, the two lattice spacings can be calculated by geometrical considerations. $d_{1}$ is:$$d_{1}=a+a\cdot \cos\left(\frac{\alpha}{2}\right)$$ $$\Rightarrow d_{1}=1.42\cdot 10^{-10}\,\text m+1.42\cdot 10^{-10}\,\text m \cdot \cos(60°)=2.13\cdot 10^{-10}\,\text m$$For \(d_2\) applies:$$d_{2}=a\cdot \sin\left(\frac{\alpha}{2}\right)$$ $$\Rightarrow d_{2}=1.42\cdot 10^{-10}\,\text m \cdot \sin(60°)=1.23\cdot 10^{-10}\,\text m$$