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 elevations of the top of the tower from these stations then prove that its inclination `theta` to the horizontal is given by `cottheta =(bcotalpha-acotbeta)/(b-a)`

Explanation

`cot theta = x/h`

`cot alpha = (a + x)/h`

`cot beta = (b + x)/h`

`cot alpha = ( a + h cot theta)/h`

`h cot alpha = a + h cot theta`

`h(cot alpha - cot theta) = a`

`h = a/(cot alpha - cot theta)`

now, `cot beta = (b+x)/h`

...