Measurement of Angles and Directions

Measurement of Angles and Directions

Angles are used to define directions. Direction is the line of sight from one point to another.

Reference Meridians

1. True Meridian: Passes through the true north and south poles.
2. Magnetic Meridian: Direction indicated by a magnetic compass needle.
3. Grid Meridian: Parallel lines on a map grid.
4. Assumed Meridian: Arbitrarily chosen direction for a specific survey.

Systems of Designating Direction

1. Azimuth

The direction of a line as given by an angle measured clockwise from the north (or south) end of a meridian. Range: $0^\circ$ to $360^\circ$.

2. Bearing

The smallest angle which the line makes with the meridian (north or south). Range: $0^\circ$ to $90^\circ$. Format: $N/S$ (Angle) $E/W$. Example: $N 45^\circ E$, $S 30^\circ W$.

Conversion: Azimuth to Bearing

• Quadrant I (0-90): Azimuth = Bearing
• Quadrant II (90-180): Azimuth = $180^\circ$ - Bearing
• Quadrant III (180-270): Azimuth = $180^\circ$ + Bearing
• Quadrant IV (270-360): Azimuth = $360^\circ$ - Bearing

Magnetic Declination ($D$)

The horizontal angle between the true meridian and the magnetic meridian.

$D = \text{Magnetic Bearing} - \text{True Bearing}$

• East Declination: Magnetic North is East of True North. Add to True Azimuth.
• West Declination: Magnetic North is West of True North. Subtract from True Azimuth.

Interior and Exterior Angles

• Interior Angle: Angle inside a closed polygon. Sum = $(n-2) \times 180^\circ$.
• Exterior Angle: Angle outside a closed polygon. Sum = $(n+2) \times 180^\circ$.
• Deflection Angle: Angle between the prolongation of the preceding line and the succeeding line.

Solved Problems