# MAPS: DIRECTION, SCALE, LATITUDE AND LONGITUDE

## AZIMUTH AND COMPASS DIRECTION

The azimuth system = Azimuth is the angular distance of an object from the local North, measured along the horizon. An object which is due North has azimuth = 0 degrees; due East is azimuth = 90 degrees; due South is azimuth = 180 degrees; due West is azimuth = 270 degrees.
The compass quadrant sytem = The compass quadrant system employs terms such as "north","northeast", "southwest", etc.

0°NORTH
Above 0° and below 90°Northeast (first quadrant)
90°EAST
Above 90° and below 180°Southeast (second quadrant)
180°SOUTH
Above 180° and below 270°Southeast (third quadrant)
270°WEST
Above 270° and below 360° or 0°Northwest (fourth quadrant)

HOW TO MEASURE AZIMUTH AND COMPASS DIRECTION
Measure the azimuth and the compass direction from Tenement Museum to Baruch Houses.
First we draw a line to link the two locations.

Then passing the point of origin (your starting point) we draw a horizontal line parallel to the horizontal edge of the black heavy border of the map.

After draw a vertical line (passing the point of origin, your starting point) parallel to the vertical edge of the black heavy border of the map.

Once you set the lines of your coordinates and the line of your angle, lay your protractor on the point of origin (your starting point). Make sure that the mid point of your protractor lines up with the point where your vertical and horizontal lines cross at the point of origin. After that starting from 90 degrees count the number of degrees that your line that links the two points is away from 90 degrees (our zero line - see the compass rose at the top of this page). If you count correctly, you will agree that we are at exactly 83.5 degrees going to the NORTHEAST direction. (83.5° NORTHEAST)

Alternative method of measuring an angle using the protractor - You draw your coordinates the same as above, but instead of laying your protractor horizontally one can lay it vertically with your starting point at zero. Make sure that the mid point of your protractor lines up with the point where your vertical and horizontal lines cross at the point of origin. After that starting from 0 degrees count the number of degrees that your line that links the two points is away from 0 degrees. If you count correctly, you will agree that we are at exactly 83.5 degrees going to the NORTHEAST direction. (83.5° NORTHEAST)

Example 1: Measure the azimuth and the compass direction from Stock Exchange to City Hall.
Once you set up your lines and coordinates, line up your protractor with the point of origin and you can see that the measurement is 36.5 degrees going Northeast. (36.5° NORTHEAST)

Alternative method of measuring an angle using the protractor - EXAMPLE 1 - You draw your coordinates the same as above, but instead of laying your protractor horizontally one can lay it vertically with your starting point at zero.Make sure that the mid point of your protractor lines up with the point where your vertical and horizontal lines cross at the point of origin. After that starting from 0 degrees count the number of degrees that your line that links the two points is away from 0 degrees. If you count correctly, you will agree that we are at exactly 36.5 degrees going to the NORTHEAST direction. (36.5° NORTHEAST)

Example 2: Measure the azimuth and the compass direction from Tribecca Film Center to South Street Seaport.
Once you set up your lines and coordinates, line up your protractor with the point of origin and you can see that the measurement is 156 degrees going Southeast (You either add 66 degrees to 90 or subtract 24 degrees from 180). (156°) SOUTHEAST

Alternative method of measuring an angle using the protractor - EXAMPLE 2 - You draw your coordinates the same as above, but instead of laying your protractor horizontally one can lay it vertically with your starting point at zero. Make sure that the mid point of your protractor lines up with the point where your vertical and horizontal lines cross at the point of origin. After that starting from 0 degrees count the number of degrees that your line that links the two points is away from 0 degrees. If you count correctly, you will agree that we are at exactly 156 degrees going to the SOUTHEAST direction. (156° SOUTHEAST)

Example 3: Measure the azimuth and the compass direction from Tenement Museum to City Hall.
Once you set up your lines and coordinates, line up your protractor with the point of origin and you can see that the measurement is 241 degrees going Southwest (You either add 61 degrees to 180 or subtract 29 degrees from 270). (241°)SOUTHWEST

Alternative method of measuring an angle using the protractor - Example 3 - You draw your coordinates the same as above, but instead of laying your protractor horizontally one can lay it vertically with your starting point at zero. Make sure that the mid point of your protractor lines up with the point where your vertical and horizontal lines cross at the point of origin. After that starting from 0 degrees count the number of degrees that your line that links the two points is away from 0 degrees. If you count correctly, you will agree that we are at exactly 119 degrees from zero. Here is where you have to remember that if you are on the left hand quadrants you have to subtract 360 - 119 = 241 degrees or you can take 180 as your point zero and count 51 degrees to the line 180 + 51 = 241 degrees going to the SOUTHWEST direction. (241° SOUTHWEST)

Example 4: Measure the azimuth and the compass direction from Tenement Museum to Soho Guggenheim.
Once you set up your lines and coordinates, line up your protractor with the point of origin and you can see that the measurement is 316 degrees going Northwest (You either add 46 degrees to 270 or subtract 44 degrees from 360). (316°) NORTHWEST

Alternative method of measuring an angle using the protractor - Example 4 - You draw your coordinates the same as above, but instead of laying your protractor horizontally one can lay it vertically. With your starting point at zero, therefore it will be easy to count. Make sure that the mid point of your protractor lines up with the point where your vertical and horizontal lines cross at the point of origin. After that starting from 0 degrees count the number of degrees that your line that links the two points is away from 0 degrees. If you count correctly, you will agree that we are at exactly 44 degrees from zero. Here is where you have to remember that if you are on the left hand quadrants you have to subtract 360 - 44 = 316 degrees or you can take 180 as your point zero and count 136 degrees to the line 180 + 136 = 316 degrees going to the NORTHWEST direction. (316° NORTHWEST)

©David Leveson and Guillermo Rocha/Brooklyn College - Earth and Environmental Sciences