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The height of a building can be determined using a theodolite. First, set up the theodolite at a distance away from the building and aim the telescope at the top of the building. Note the horizontal angle (the angle from the theodolite to the top of the building).
Move the theodolite to another location and take a measurement from there. Calculate the difference in angle between the two observations. The change in horizontal angle multiplied by the distance between the two locations will give you the height of the building.