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Question id: 231. This question is similar to one that appeared in a GCSE Higher paper in 2005. The use of a calculator is allowed.

Bearings Loci

A fishing boat is somewhere along the line from A to C.

Fishing for Lobsters

(a) By measuring an angle, write down the three-figure bearing of the boat from A.

(b) The coastguard at B sees the ship on a bearing of 047°. On the diagram draw accurately the line showing a bearing of 047° from B.

(c) On the diagram mark the position of the fishing boat, F.

(d) Measure the length, in centimetres, of the line AB on the diagram.

(e) The distance from A to B is 12 kilometres. Calculate the scale of your copy of the map. Give your answer in the form 1 : n.

(f) There is a lighthouse at A. The range of the light from the lighthouse is 9.6 kilometres. Using your scale, draw the locus of points that are 9.6 kilometres from A.

(g) The boat is sailing straight for a lobster pot attached to a buoy at D. Draw the line FD on the diagram. How far is the boat from the lobster pot when the light from the lighthouse is first seen on the boat? Give your answer in kilometers correct to the nearest 100 metres.

(h) If the boat does not alter course it will arrive at D after 30 minutes. Calculate the speed of the boat in kilometers per hour.

(i) A knot is 1 nautical mile per hour. One nautical mile is equal to 1.85 kilometres. Calculate the speed found in part (h) in knots. Give your answer to one decimal place.

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