Calculation example - Calculate the height of an object when its top and bottom are visible but inaccessible #2

Calculate the height of an object from a baseline when its top and bottom is visible but not accessible from observation points. Case scenario when baseline AB on sloping ground and in line with object.

Known values:

Baseline distance AB length, height h₁ of the observer at points A and B.

Vertical angles measured at A – α₁, a₂ and δ.

Vertical angles measured at B – β₁ and β₂.

Solution: Height of object Η.

First, measure horizontal distance AB and vertical angles α₁, α₂, δ and β₁, β₂ from observer points A₁ and B₁ respectively.

In triangle A₁ΕB₁,

Same for triangle A₁OB₁,

Then calculate sloping distance A₁Ε:

and

Same for sloping distance A₁O:

and

Then:

Thus: