Trigonometry - OCRSolve problems using sine and cosine rule- Higher
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.
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
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
Example
Ship A leaves port P and travels on a bearingA direction measured in degrees clockwise from North. Due North is 000, due East is 090, due South is 180 and due West is 270. of 200掳. A second ship B leaves the same port P and travels on a bearing of 165掳. 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 = \(200 - 165 = 35^\circ\).
Two sides and the angle in between are known. Calculate the length AB.