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Firefighter Math: 6.6 Vectors

A vector has a magnitude (often representing distance or speed) and direction. When a clinometer (see Section 4.5) is used to estimate the slope percent and the slope length is measured with a metal tape, the result is a vector. The slope length represent the magnitude and the slope percent can be converted into a slope angle that represents direction. Vectors can provide information about the distance and direction of fire spread, or the speed and direction of fire spread or wind. 

Firefighter Math: 6.5 Declination

The magnetic reference for Earth is north regardless of whether you are traveling north or south. Magnetic declination, or declination, is the difference between the true north reading from the map and the magnetic north reading from a compass. When a compass is used in combination with a map, a correction must be made to allow for declination.

Firefighter Math: 6.4 Compass

A compass is an instrument used to determine direction in fire control work. An azimuth compass is graduated/marked with a full circle of 360 degrees called an azimuth circle. Compass components include a magnetic needle that always points to magnetic north, a graduated circle for laying off angles from true north, and a sighting line for extending a line of sight while following a course of direction. The north end of the needle is marked with a small arrow. 
 

Firefighter Math: 6.3 Back Azimuth and Backsighting

A back azimuth is a projection of the azimuth from the origin to the opposite side of the azimuth circle. There are 360 degrees in the azimuth circle, so the opposite direction would be 180 degrees (half of 360 degrees) from the azimuth.

A back azimuth is calculated by adding 180° to the azimuth when the azimuth is less than 180°, or by subtracting 180° from the azimuth if it is more than 180°. For example, if an azimuth is 320°, the back azimuth would be 320° - 180° = 140°. If the azimuth is 30°, the back azimuth would be 180° + 30° = 210°.

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