Calculation example - Calculate the height of an object when its base is inaccessible #3

Calculate the height of an object from a baseline when its projected position to the ground is inaccessible. Case scenario when baseline AB on sloping ground and collinear with object.

Known values:

Baseline sloping distance AB and height h₁ of the observer.

Angles measured at A – Vertical angles α and δ (slope of ground between A and B).

Angle measured at B – Vertical angle β. 

Solution: Height of object above ground at position A. 

First, measure sloping distance AB.  From observer point A₁, measure vertical angles α and δ. From observer point B₁, measure vertical angle β.

In triangle A₁ΟB₁,

Then calculate sloping distance A₁O:

Finally, calculate height of object above ground at station A: