Chapter 9.1
Pythagoras' Theorem (Finding Hypotenuse)
Use a² + b² = c² to find the longest side (hypotenuse) in right-angled triangles.
Chapters17
Right-angled triangles, 3D applications, sine/cosine rules.
Time invested13 hrs
Approximate guided learning.
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Chapter 9.2
Pythagoras' Theorem (Finding Shorter Side)
Rearrange Pythagoras to find one of the shorter sides when given the hypotenuse.
Chapter 9.3
Pythagoras' Theorem (Problem-Solving)
Apply Pythagoras to real-world contexts: ladders, diagonals, distances, and more.
Chapter 9.4
Pythagoras in 3D (Higher)
Find lengths in 3D shapes: cuboids, pyramids, and complex structures.
Chapter 9.5
Trigonometry Introduction (SOH CAH TOA)
Learn the fundamental trigonometric ratios: sine, cosine, and tangent.
Chapter 9.6
Finding Sides Using Trigonometry
Use sin, cos, and tan to calculate unknown sides in right-angled triangles.
Chapter 9.7
Finding Angles Using Trigonometry
Use inverse trig functions (sin⁻¹, cos⁻¹, tan⁻¹) to find unknown angles.
Chapter 9.8
Trigonometry Problem-Solving (2D)
Apply trigonometry to real-world problems: angles of elevation, depression, and more.
Chapter 9.9
Trigonometry in 3D (Higher)
Find angles and lengths in 3D shapes using combined Pythagoras and trigonometry.
Chapter 9.10
Exact Trigonometric Values (Higher)
Learn exact values for sin, cos, and tan of 0°, 30°, 45°, 60°, and 90°.
Chapter 9.11
Sine Rule (Higher)
Use a/sin A = b/sin B = c/sin C to find sides and angles in ANY triangle.
Chapter 9.12
Cosine Rule (Higher)
Use a² = b² + c² - 2bc cos A to solve triangles with no right angle.
Chapter 9.13
Area of Triangles (½ab sin C) (Higher)
Find the area of any triangle using the formula Area = ½ab sin C.
Chapter 9.14
Sine and Cosine Rule Problem-Solving (Higher)
Tackle complex multi-step problems requiring both sine and cosine rules.
Chapter 9.15
Trigonometry and Bearings
Combine bearings with trigonometry for navigation and surveying problems.
Chapter 9.16
Trigonometric Graphs (y = sin x, cos x, tan x) (Higher)
Sketch and interpret graphs of sine, cosine, and tangent functions.
Chapter 9.17
Trigonometry Mastery (GCSE)
Master all trigonometry topics with exam-style questions and mixed practice.
Next steps
Ready for more geometry? Continue to Section 10 for transformations and vectors, or revisit Section 8 for foundational geometry.