# Trigonometry questions

1) A herring gull was ringed at Llyn Trawsfynydd Gwynedd (grid reference SH 700360) and was retapped near Criccieth, Gwynedd ( grid reference SH 500380). The ringing report states the Distance as 20km and the Direction as 276 degrees.

(a) Use the grid references and trigonometry to check that the map bearing of Criccieth from Llyn- Trawsfynydd is the value reported as Direction on the ringing report.

2) Another herring gull also ringed at Llyn Trawsfynydd, was found at Barmouth. The finding place is 23km from Llyn Trawsfynydd on a bearing of 203 degrees.

(a) Explain how to use cosine formula to calculate the distance between Criccieth and Barmouth. Do the calculation, showing your working and rounding your answer appropriately.

(b) Use the sine formula to calculate the size of the angle at Criccieth that is formed by the line joining Barmouth to Criccieth and the line joining Llyn Trawsfynydd to Criccieth.

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#### Solution Summary

This solution assists with the problems regarding the Pythagoras theorem, cosine and sine formulas.