how to Calculate the height of an object using With theodolite

Calculate the height of an object using With Theodolite

Let us proceed with the calculation of building’s height by utilizing a theodolite, as illustrated in the diagram provided. how to Calculate the height of an object using With theodolite.

Begin by ensuring the theodolite is leveled on the vertical axis and set to 0° on the horizontal axis, indicated by a dotted line. Measure the distance (L) from the theodolite station point to the building as depicted in the illustration.

Bisect the top edge corner of the building using the theodolite and record the angle value θ1. Repeat this process for bottom edge corner, noting the angle value θ2.

Reconstruct the triangles with measured angle values for the calculation purposes.

Label triangle one as ABC, with A representing the theodolite station point.

Given Data

Angle θ1 = 34° 7′

Length of AB = L = 72m.

From trigonometry,

Tan θ1 = (opposite side ÷ adjacent side )

= (side BC ÷ side AB)

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Tan 34° 7′  = h1 ÷ 72m.

h1 =  tan 34° 7′ × 72m.

= 0.67747 × 72m

= 48.778m.

Triangle two shall be designated as ABD, with A representing the theodolite station point.

Given Data

Angle θ2 = 1° 12′

Length AB = L = 72m.

From trigonometry,

Tan θ2 = ( opposite side ÷ adjacent side )

= side BD ÷ side AB

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Tan 1° 12′

= h2 ÷ 72m.

h2          =  tan 1° 12′ × 72m.

= 0.02094 × 72m

                = 1.508m.

Now, the height of the building

H          = [h1 + h2]

= [48.778m. + 1.508m.]

                = 50.286m.

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