The three trigonometric ratios; sine, cosine and tangent are used to calculate angles and lengths in right-angled triangles. The sine and cosine rules calculate lengths and angles in any triangle.

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To solve problems involving non-right-angled triangles, the correct rule must first be chosen.

The cosine rule can be used in any triangle to calculate:

- a side when two sides and the angle in between them are known
- an angle when three sides are known

The sine rule can be used in any triangle to calculate:

- a side when two angles and an opposite side are known
- an angle when two sides and an opposite angle are known

Ship A leaves port P and travels on a bearing of 200°. A second ship B leaves the same port P and travels on a bearing of 165°. After half an hour ship A has travelled 5.2 km and ship B has travelled 5.8 km. How far apart are the ships after half an hour? Give the answer to three significant figures.

Remember a bearing is an angle measured clockwise from north. The angle APB = .

Two sides and the angle in between are known. Calculate the length AB.

Use the cosine rule.

AB = 3.36 km