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Free lesson on True bearings and compass bearings, taken from the Trigonometry topic of our NSW Senior Secondary (HSC) (new courses) Year 12 textbook. Learn with worked examples, get interactive applets, and watch instructional videos.
- What Is A Bearing in Mathematics?
- How to Calculate A Bearing
- How to Calculate A Bearing from An Angle
- How to Calculate A Bearing Using Trigonometry
- Bearings with Vectors
In mathematics, a bearing is defined as an angle measured clockwise from north. Bearings are usually written as a three-figure bearing. For example, the angle 50° from north is written as 050°. A bearing is always defined as an angle clockwise from north. Bearings are important for navigation in 2-dimensions such as when using maps. Bearings are us...
To calculate a bearing, find the angle clockwise from north. Start by drawing a vertical line representing north at the first location. Draw a line connecting the start location to the end location. Measure the clockwise angle between the north line and this line. For example, the bearing from A to B is 100°. This is the angle from north clockwise ...
Bearing From an Interior Angle
Interior angles add to 180°. If given the bearing from B to A, the bearing from A to B can be found using interior angles. Subtract the bearing of B to A from 180° to find the missing interior angle, then use the fact that angles in a full turn add to 360° to find the bearing of A to B. For example, the bearing of B from A is 050°. Find the bearing of A from B. Drawing a north on both points A and B, the norths form parallel lines and a co-interior angle are formed. The bearing of 050° and th...
Bearings with Alternate Angles
Alternate angles are equal and are recognised by the ‘z’ shape made between the two angles. These angle facts can be used to calculate bearings. For example, find the bearing of B from A. The angle of 120° is shown. It makes an alternate angle with the bearing of B from A. Therefore the bearing of B from A is also 120°. Here is another example of using alternate angle facts to find a bearing. Find the bearing of B from A We can see that alternate angles are equal. Therefore the angle between...
To find a bearing using trigonometry, create a right-angled triangle. If distances are given in any of the compass directions, label these sides as the adjacent or opposite sides of the triangle. If a distance is given in a particular bearing, label this distance as the hypotenuse of the triangle. For example, a man walks 10 km east and then 6 km n...
For any vector of the form ai+bj, the angle of the vector is found using tan-1(b/a). The bearing of the vector is then found as the angle clockwise from north. For example, the vector (3i-4j) makes an angle of tan-1(4/3) = 53° below east. The bearing is found as 90°+53°=143°. Vectors can be written as bearings since: A positive icomponent is in the...
Solution. First I would draw a diagram. The bearing needed is the angle marked with the blue arc. It is clockwise from north. 2. Use trigonometry to write an equation and solve it for θ, the bearing. 3km is opposite θ. 6km is adjacent to θ. So the trig ratio we need is tan.
Bearings maths GCSE questions. 1. The bearing of A from B is 215^ {\circ} 215∘. Find the bearing of B from A. (2 marks) Show answer. 2. The point C is on a bearing of 065^ {\circ} 065∘ from point A and on a bearing of 310^ {\circ} 310∘ from point B. On the diagram, mark with a (x) (x) the position of point C.
The four main compass bearings (North, East, South and West) are multiples of 90°: The advantage of three-figure bearings is that they describe any direction uniquely: Note that the last one has four figures (three in front of the decimal point and one after) but it is still a "three-figure bearing", the .4 just gives more accuracy.
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People also ask
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The bearing of a point is the number of degrees in the angle measured in a clockwise direction from the north line to the line joining the centre of the compass with the point. A bearing is used to represent the direction of one point relative to another point. For example, the bearing of A from B is 065º.
