The Sine and Cosine Rules

1. Right-angled triangle trigonometry
2. Bearings
3. Trigonometry with obtuse angles
4. The sine rule
5. Using the sine rule to find an unknown
6. The cosine rule
7. Using the cosine rule to find an unknown
8. Area of a triangle
9. Applications of the sine and cosine rule
10. Offset and radial surveys

The syllabus can be found here (page 90)

• draw diagrams to represent information given about a right-angled triangle
• solve problems using trigonometric ratios in one or more right-angled triangles
• solve problems involving angles of elevation and depression, given the appropriate diagram
  

Some students:

• Memorise the initials SOH CAH TOA, or
  
• Use a pneumonic

• use compass bearings (eight points only) and true bearings (three-figure bearings) in problem-solving related to maps and charts
  

Bearings use angles to show the direction of one location from a given point

True bearings or three-figured bearings are measured in a clockwise direction from true north 000 to 360

Compass bearings refer to the eight compass points: N, NE, E, SE, S, SW, W, NW.

• establish the sine, cosine and tangent ratios for obtuse angles using a calculator
• determine the sign of the above ratios for obtuse angles
  

You need to be able to establish the sine, cosine and tangent ratios for obtuse angles using a calculator

• determine the sign of the above ratios for obtuse angles
• use the sine rule to find side lengths and angles of triangles
  

The sine rule is a relationship between the two of the sides of triangles and two of the angles.

• use the cosine rule to find side lengths and angles of triangles
  

The cosine rule is a relationship between three sides of a triangle and one of its angles

• use the cosine rule to find side lengths and angles of triangles
  

• calculate the area of a triangle using the formula A = 1/2 absinC

The area of a triangle can be calculated in trigonometry by using the following formula:

• use appropriate trigonometric ratios and formulae in ‘two-triangle problems’, where one triangle is right-angled and the diagram is given
• select and use appropriate trigonometric ratios and formulae to solve problems involving right-angled and non-right-angled triangles
  

• conduct radial (both plane table and compass) surveys
• solve problems involving non-right-angled triangle trigonometry, Pythagoras’ theorem, and area in offset and radial surveys
  

Surveying involves setting out the positions of proposed construction or engineering works. It involves the measurements of boundaries of a field and the calculation of perimeter of areas. There are a number of surveying techniques, including:

• Offset survey (preliminary course)
• Simpson's rule (chapter three)
• Plane table radial survey
• Compass radial survey
• Triangulation

Plane table radial survey

A table is placed in the middle of a field and the distances to each corner are measured and marked on a large sheet of paper pinned tot he desk. The word 'radial' means coming out of a central point, like a radius or a ray.

Compass radial survey

Similar to a plane table survey except that each corner is measured by a compass placed in the middle of the field