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Using trigonometry and the provided bearings, calculate the distance and bearing of B from C. Assume AB=100m and AC=120m.

Mathematics

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Item One.

a) Measure the distance and bearing of B from C
Since an accurate scale drawing cannot be performed here, we will use trigonometry (the Cosine Rule and Sine Rule) to calculate the distance and bearing.

  1. Determine the angle ∠BAC\angle BAC.

    The bearing of B from A is 058∘058^\circ.
    The bearing of C from A is 082∘082^\circ.
    The angle between AB and AC at point A is the difference between these bearings.

    ∠BAC=082∘−058∘=24∘\angle BAC = 082^\circ - 058^\circ = 24^\circ

  2. Calculate the distance BC using the Cosine Rule.

    Given:

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