The lines of length … and … meet at the angle

Problems, on the attraction of a sphere, use Figure 14.18 and the law of cosines $q^2=D^2-2\rho D\cos \varphi +{\rho }^2=u$.

The lines of length $D$ and $q$ meet at the angle $\alpha$. Move the meeting point up by $\Delta D$. Explain why the other line stretches by $\Delta q\approx \Delta D\cos \alpha$. So $\partial q/\partial D=\cos \alpha$ as before.

Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) · §14.4 Cylindrical and Spherical Coordinates, #28