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In surveying, bearings can be referenced to true north, magnetic north, grid north (the Y axis of a map projection), or a previous map, which is often a historical magnetic north. [citation needed] If navigating by gyrocompass, the reference direction is true north, in which case the terms true bearing and geodetic bearing are used.
With a local declination of 14°E, a true bearing (i.e. obtained from a map) of 54° is converted to a magnetic bearing (for use in the field) by subtracting declination: 54° – 14° = 40°. If the local declination was 14°W (−14°), it is again subtracted from the true bearing to obtain a magnetic bearing: 54°- (−14°) = 68°.
A bearing compass, is a nautical instrument used to determine the bearing of observed objects. (Bearing: angle formed by the north and the visual to a certain object in the sea or ashore). Used in navigation to determine the angle between the direction of an object and the magnetic north or, indirectly relative to another reference point.
For example, a bearing might be described as "(from) south, (turn) thirty degrees (toward the) east" (the words in brackets are usually omitted), abbreviated "S30°E", which is the bearing 30 degrees in the eastward direction from south, i.e. the bearing 150 degrees clockwise from north.
In navigation, a rhumb line, rhumb (/ r ʌ m /), or loxodrome is an arc crossing all meridians of longitude at the same angle, that is, a path with constant azimuth (bearing as measured relative to true north). Navigation on a fixed course (i.e., steering the vessel to follow a constant cardinal direction) would result in a rhumb-line track.
Fig. 1 – A triangle. The angles α (or A), β (or B), and γ (or C) are respectively opposite the sides a, b, and c.. In trigonometry, the law of cosines (also known as the cosine formula or cosine rule) relates the lengths of the sides of a triangle to the cosine of one of its angles.
In trigonometry, the law of sines, sine law, sine formula, or sine rule is an equation relating the lengths of the sides of any triangle to the sines of its angles. According to the law, = = =, where a, b, and c are the lengths of the sides of a triangle, and α, β, and γ are the opposite angles (see figure 2), while R is the radius of the triangle's circumcircle.