# Exam-Style Question on Trigonometry

## A mathematics exam-style question with a worked solution that can be revealed gradually

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Question id: 389. This question is similar to one that appeared on an IB AA Standard paper (specimen) for 2021. The use of a calculator is allowed.

Emma sails in a small dinghy from point A in a straight line to a buoy at point B. She is moving at an average speed of 19 km/h, for 6 minutes, on a bearing of 125°.

(a) Find the distance from point A to point B

(b) When Emma arrives at point B she changes direction and sails to point C on a bearing of 230° and one 1 km away. Find angle ABC

(c) Find the distance from point A to point C.

(d) Find angle BCA

(e) Emma’s friend Eamonn wants to swim directly from point A to point C. Find the bearing that Eamonn must take to point C.

(f) Eamonn swims at an average speed of 3.2 km/h. Find, to the nearest minute, the time it takes for Eamonn to reach point C.

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If you need more practice try the self-checking interactive exercises called Advanced Trigonometry.

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