Surveying I– coordinate account

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Replacement of angular measure

The measure is called the angular size of the angle in the appropriate unit. Due to the ease of making calculations in surveying the most common measure is the measure of hail.

Use the following ratio can easily convert angular measurements. Next to each model is an example.

Degrees	Centesimal degrees	Radians
Full angle: 360˚ Division into smaller parts: 1˚=60’ 1’=60’’ 1˚=3 600’’	Full angle: 400g Division into smaller parts: 1g=100c 1c=100cc 1g=10 000cc	Full angle: 2π rad

Note: Before the conversion of angles to measure the progressive part of the minutes and seconds must be converted into decimal degrees

degrees → centesimal degrees
α˚ – α^g
360˚ – 400^g


α^g = α˚• 400^g 360˚


α^g = α˚ 10^g 9˚

Example

Replace degree angle to angle in centesimal degree.

Data:
α˚ = 56˚45'31"

SOLUTION

56˚45'31" = 56˚ + ( 45 60 )˚ + ( 31 3600 )˚ = 56˚ + 0,750000˚ + 0,008611˚ = 56˚,758611

α^g = 56˚,758611 • 10^g 9˚ = 63^g,065123 = 63^g06^cc51^cc

degrees → radians
α˚ – α
360˚ – 2π rad


α = α˚• 2π rad 360˚


α = α˚ π rad 180˚

Example

Replace degree angle to angle in radians.

Data:
α˚ = 6˚41'01"

SOLUTION

6˚41'01" = 6˚ + ( 41 60 )˚ + ( 1 3600 )˚ = 6˚ + 0,683333˚ + 0,000278˚ = 6˚,683611

α = 6˚,683611 • π rad 180˚ = 0,116651rad

centesimal degrees → degrees
α^g – α˚
400^g – 360˚


α˚ = α^g • 360˚ 400^g


α˚ = α^g 9˚ 10^g

Example

Replace centesimal degree angle to angle in degree.

Data:
α^g = 310^g88^c97^cc

SOLUTION

α˚ = 310^g,8897 • 9˚ 10^g = 279˚,800730 = 279˚ + 0,800730•60' = 279˚ + 48' + 0,043800•60" = 279˚48'02,6"

centesimal degrees → radians
α^g – α
400^g – 2π rad


α = α^g • 2π rad 400^g


α = α^g π rad 200^g

Example

Replace centesimal degree angle to angle in radians.

Data:
α^g = 54^g66^c25^cc

SOLUTION

α = 54^g,6625 • π rad 200^g = 0,858637rad

radians → degrees
α – α˚
2π rad – 360˚


α˚ = α • 360˚ 2π rad


α˚ = α 180˚ π rad

Example

Replace radian angle to angle in degree.

Data:
α = 3,14159rad

SOLUTION

α˚ = 3,14159rad • 180˚ π rad = 179˚,999848 = 179˚ + 0,999848•60' = 179˚ + 59' + 0,990878•60" = 179˚59'59,5"

radians → centesimal degrees
α – α^g
2π rad – 400^g;


α^g = α • 400^g 2π rad


α˚ = α 200^g π rad

Example

Replace radian angle to angle in centesimal degree.

Data:
α = 1,35227rad

SOLUTION

α˚ = 1,35227rad • 200^g π rad = 86^g,088182 = 86^g08^c82^cc