Chapter 9.1
Pythagoras' theorem (introduction)
Discover the famous formula a² + b² = c². Learn to identify right-angled triangles and find the hypotenuse.
Chapters15
Pythagoras, trigonometry, sine rule, cosine rule, applications.
Time invested11 hrs
Approximate guided learning.
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Chapter 9.2
Pythagoras' theorem (finding the hypotenuse)
Practice finding the longest side (hypotenuse) of right-angled triangles using c² = a² + b².
Chapter 9.3
Pythagoras' theorem (finding a shorter side)
Learn to find the length of a shorter side when you know the hypotenuse using a² = c² - b².
Chapter 9.4
Pythagoras' theorem (problem-solving)
Apply Pythagoras to real-world problems: ladders, diagonals, coordinates, and GCSE questions.
Chapter 9.5
Pythagoras in 3D
Extend Pythagoras to three dimensions: cuboids, pyramids, and space diagonals.
Chapter 9.6
Introduction to trigonometry (SOH CAH TOA)
Learn the revolutionary SOH CAH TOA: sine, cosine, and tangent ratios for right-angled triangles.
Chapter 9.7
Finding sides using trigonometry
Use sin, cos, and tan to find missing sides in right-angled triangles.
Chapter 9.8
Finding angles using trigonometry
Use inverse trigonometry (sin⁻¹, cos⁻¹, tan⁻¹) to find missing angles.
Chapter 9.9
Trigonometry problem-solving
Apply trigonometry to real-world contexts: heights, distances, angles of elevation and depression.
Chapter 9.10
Trigonometry in 3D
Extend trigonometry to three-dimensional problems combining Pythagoras and SOH CAH TOA.
Chapter 9.11
Exact trigonometric values
Learn the exact values for sin, cos, and tan of 30°, 45°, and 60° (GCSE Higher).
Chapter 9.12
Sine rule
Solve ANY triangle (not just right-angled) using the sine rule: a/sinA = b/sinB = c/sinC.
Chapter 9.13
Cosine rule
Use the cosine rule to find sides or angles in any triangle: a² = b² + c² - 2bc cosA.
Chapter 9.14
Area of triangles using trigonometry
Calculate the area of ANY triangle using Area = ½ab sinC (GCSE Higher).
Chapter 9.15
Trigonometry applications (bearings, navigation)
Apply all trigonometry skills to bearings, navigation, and complex GCSE problems.
Next steps
Ready to explore transformations? Move on to Section 10 or revisit Section 8 for foundational geometry concepts.