Calculation example - Calculate the height of an object when its base is inaccessible #2

Calculate the height of an object from a baseline when its projected position to the ground is inaccessible. Case scenario when baseline AB is level but 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 and vertical angle α

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

Solution: Height of object above ground at position A.

In triangle ABC, given the sine law:

Then

Also

Thus:

Ηeight of object (Ε) above ground at station A = C₁E + h₁

and

Ηeight of projection (D) above ground at station A = C₁E + h₁ - h₂ if height h₂ is known.