Pythagoras and Trigonometry.
Connect the geometry of right triangles with side ratios, then solve practical problems with clear models and interpreted answers.
Work through the topic
Learn the method, follow the examples, then try the worksheet.
- 01
Pythagoras review
Use the sides of a right triangle to find a missing length and check a proposed right angle.
- 02
Exact/rounded missing lengths
Keep square-root answers exact and round only at the requested final step.
- 03
Opposite, adjacent and hypotenuse
Name sides relative to a chosen acute angle, whatever the orientation of the triangle.
- 04
Similarity and fixed trigonometric ratios
Use similarity to explain why right-triangle ratios depend on an angle rather than size.
- 05
Sine, cosine and tangent
Choose sine, cosine or tangent from the two side types involved.
- 06
Finding a side
Solve for a side using one acute angle and one known side.
- 07
Finding an angle
Recover an acute angle from two sides using an inverse trigonometric function.
- 08
Selecting the right method
Choose Pythagoras, a trigonometric ratio or an inverse ratio from the information given.
- 09
Practical right-triangle problems and interpreting diagrams
Build a labelled right-triangle model and distinguish total height from height changes.
Topic review
Revisit the key ideas, then choose a practice paper.