## ANGLE MEASUREMENTS

### MEASURING BY REPETITION

Measure the angle (e.g. 73° 21')
Tighten the lower motion clamp
Re-sight on the initial point
Sight the second point and re-measure the angle (e.g. 146° 44')
Repeat process as many times as desired
Solution equals the average of the measurements, or the final measurement divided by the number of measurements
### REPEATING MEASUREMENTS

1st measurement: 73° 21'
2nd measurement: 146° 44'
3rd measurement: 220° 06'
4th measurement: 293° 29'
5th measurement: 6° 49' (you have gone past 360°, so this is like 366° 49')
6th measurement: 80° 12' (this is like 440° 12')
average angle measurement:

(80° 12' + 360° ) / 6 = 73° 22'

### CLOSING THE HORIZON

### AZIMUTHS

Azimuths are angles that are measured clockwise from a reference direction
The reference direction need not be true north or magnetic north
Azimuth angles range from 0° to 360°
### MEASURING VERTICAL ANGLES

Angles above or below a horizontal through the point of observation (line of sight)
Angles above the horizontal plane are called
plus angles

angles of elevation

Angles below the horizontal plane are called
minus angles

angles of depression

Theodolites measure zenith angles
### ZENITH ANGLES

a reading of 0° corresponds to the telescope pointing vertically (or towards the zenith)
the telescope in a horizontal position would read a zenith angle of 90°
an angle read with the telescope elevated 30° above the horizon would read a zenith angle of 60°

A graphic of an Electronic Digital Theodolite is available.