# Solving problems using the sine and cosine rule - Higher

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, eg a, b and C
• an angle when three sides are known, eg a, b and c

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

• a side when two angles and an opposite side are known, eg a, A and B
• an angle when two sides and an opposite angle are known, eg a, A and b

### Example

Ship A leaves port P and travels on a of 200°. A second ship B leaves the same port P at the same time 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