Surveying
If θ and δ be the latitude of an observer and declination of a heavenly body respectively, the upper culmination of the body will be south of zenith if its zenith distance, is

½ (θ - δ)
δ - θ
θ + δ
θ - δ

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Surveying
Theodolite is an instrument used for

measurement of vertical angles only
measurement of horizontal angles only
measurement of both horizontal and vertical angles
tightening the capstan-headed nuts of level tube

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