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Bearings

Bearings involve using trigonometry, generally the cosine or sine rules:

Cosine Rule:

Sine Rule:

For the above diagram, find

a)The distance BC

b)The bearing of A from B and the bearing of A from C.

a)Label the triangle as above, with sides labelled by little letters opposite angles labelled by big letters.

so

b)

We draw a right angled triangle between A and B. Construct a right angled triangle at A and a horizontal line starting from A to the right.The internal angles of the right angled triangle are 70 and 20 degrees. Hence the bearing of A from B is 360-20=340 degrees.

To find the bearing of A from C, use the Sine Rule to find C.

Construct the right angled triangle as shown, with the angles at C then the bearing is 56+32.75=88.75 degrees.

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