## 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'

### 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.