You can do that without derivatives, integrals, complex numbers, sines, cosines, tangents, exponentials, square roots, or even addition and subtraction. If the pole is plumb, erect a pole smaller than you with a plumb bob, measure its length a and its shadow's length b, and then calculate the height of the original pole from its shadow's length c as ac/b.

If you have a slide rule, you can do this in a single motion: align c on the C scale over b on D and read off the answer on C above a on the D scale.