Mathematics

Problem

Two stations due South of a leaning tower, which leans towards the North, are at distances

a

and

b

from its foot. If

\alpha

and

\beta

are the angles of elevation of the top of the tower from these stations, prove that its inclination

\theta

to the horizontal is given by

\cot \theta = \frac{b \cot \alpha - a \cot \beta}{b - a}