Practical trigonometry.
Use similarity, triangle geometry and trigonometric rules to solve practical measurement and navigation problems, then check that each answer fits the context.
Work through the topic
Learn the method, follow the examples, then try the worksheet.
- 01
Similarity and scale
Use matching sides and scale factors to transfer lengths and areas between similar figures.
- 02
Right-triangle geometry
Read a right-triangle diagram accurately before selecting a length or angle method.
- 03
Pythagoras
Find unknown lengths using Pythagoras and check that the result fits the triangle.
- 04
Sine/cosine/tangent
Choose a trigonometric ratio to find a side or acute angle in a right triangle.
- 05
Elevation/depression and bearings
Model height and navigation problems using horizontals, verticals and bearings.
- 06
Triangle area
Find triangle areas using a perpendicular height or two sides and their included angle.
- 07
Sine rule
Use opposite side-angle pairs and check whether SSA data allow zero, one or two triangles.
- 08
Cosine rule
Use the cosine rule for two sides with their included angle, or for three known sides.
- 09
Non-right-triangle surveying/navigation problems
Build and solve triangle models for surveying, inaccessible distances and routes.
- 10
Checking possible solutions
Check triangle existence, candidate angles, precision and contextual reasonableness.
Topic review
Revisit the key ideas, then choose a practice paper.