Alternative (table-interpolation) route — avoid a calculator's inverse-tangent key and instead use a standard tangent table:
\(\tan30^\circ=0.5774\), \(\tan31^\circ=0.6009\). Our target value \(\tan\lambda=0.5959\) lies between these two, closer to 31\(^\circ\):
\[ \text{fraction}=\dfrac{0.5959-0.5774}{0.6009-0.5774}=\dfrac{0.0185}{0.0235}\approx0.79 \]
\[ \lambda\approx30^\circ+0.79^\circ=30.79^\circ \]
This confirms \(\lambda\approx30.8^\circ\) obtained above by direct inversion.
Distance \(=30.79\times111=3417.7\) km \(=3.4177\times10^{8}\) cm.
Rate \(=\dfrac{3.4177\times10^{8}}{1.4\times10^{8}}\approx2.44\) cm/yr — the identical result via a purely tabular interpolation, safely inside the 2.3–2.5 cm/yr key range.