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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:
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