IB Maths AI SL AI 3.1 practice question

Question 1

Paper 2Medium6 marks

Two coastal stations, $A$ and $B$ lie on a straight east–west coastline. Station $B$ is $5.7\text{ km}$ due east of station $A$ A boat at $C$ north of the coastline, is observed on a bearing of $062^\circ$ from $A$ and a bearing of $323^\circ$ from $B$

(a)

Draw a labelled sketch of the situation and determine the interior angles of triangle $ABC$ at $A$ and $B$

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(b)

Determine the distance $AC$ giving your answer to 3 significant figures.

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(c)

Hence, using your answer to part (b), determine the shortest distance from the boat to the coastline. Give your answer to 3 significant figures.

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