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

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 is horizontal 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 and a₂.

Vertical angles measured at B – β₁ and β₂.

Solution: Height of object Η.

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

Then calculate vertical distances C₁E and C₁O.

Thus:

Also:

Thus:

Combining the previous equations: