Calculation example - Calculate the height of an object when its base is inaccessible #4

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 not in line with object.

Known values:

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

Angles measured at A – Horizontal angle θ vertical angle α to object, and vertical angle δ slope of ground.

Angles measured at B – Horizontal angle φ and vertical angle β.

Solution: Height of object above ground at position A.

First, calculate horizontal distance A₁B₂.

In triangle A₁C₁B₂, given the sine law:

In triangle A₁C₁E:

Then:

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

Combining the previous: