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Find the bearing of: a) A, from B. b) B, from A.

Mathematics

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Answers

2 parts
a

144∘144^\circ

b

324∘324^\circ

Step-by-step solution

4 steps

Here's how to solve the problem based on the diagram:

Part a· 1 step

Find the bearing of A from B.

  1. Identify the given bearing from the diagram.

    The diagram shows point B with a North line. The angle measured clockwise from the North line at B to the line segment BA is given as 144∘144^\circ. This is the definition of the bearing of A from B.

    The bearing of A from B is 144°.

    144∘\boxed{144^\circ}

Part b

324∘324^\circ

Find the bearing of B from A.

  1. Understand that this is a back bearing problem.

    We are given the bearing of A from B (144∘144^\circ) and need to find the bearing of B from A. This is the back bearing.

  2. Apply the rule for calculating back bearing.

    To find the back bearing, if the original bearing is less than 180∘180^\circ, add 180∘180^\circ. If the original bearing is greater than 180∘180^\circ, subtract 180∘180^\circ.
    The bearing of A from B is 144∘144^\circ, which is less than 180∘180^\circ.

  3. Calculate the back bearing.

    Bearing of B from A=Bearing of A from B+180∘\text{Bearing of B from A} = \text{Bearing of A from B} + 180^\circ Bearing of B from A=144∘+180∘\text{Bearing of B from A} = 144^\circ + 180^\circ Bearing of B from A=324∘\text{Bearing of B from A} = 324^\circ

    The bearing of B from A is 324°.

    324∘\boxed{324^\circ}
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