Pythagoras theorem is one of the most searched IGCSE maths topics because it appears in geometry and applied questions. For a right-angled triangle: (a^2 + b^2 = c^2) where (c) is the hypotenuse. You need to identify the right angle, label sides, substitute correctly, and round to the required accuracy.

When to Use Pythagoras

• Two sides known → find the third (rearrange: (a = \sqrt{c^2 - b^2}) etc.).
• Hypotenuse is always the longest side, opposite the right angle.
• 3D: Often you form a right-angled triangle (e.g. diagonal of a cuboid = base diagonal and height); apply Pythagoras once or twice.
• Word problems: Draw a diagram; identify the right-angled triangle and which side you need.

Common Mistakes

• Using the wrong side as hypotenuse.
• Forgetting to square and take square root (e.g. writing (a + b = c)).
• Wrong rounding (e.g. 3 s.f. or 1 d.p. as requested).

Tutopiya’s IGCSE Maths tutors can help you apply Pythagoras confidently in 2D and 3D.

Worked Example and Where Pythagoras Appears

Example: Right-angled triangle with a = 5 cm, b = 12 cm. Find c. c² = a² + b² = 25 + 144 = 169, so c = 13 cm. For 3D (e.g. diagonal of a cuboid), find a right-angled triangle (e.g. base diagonal and height) and apply Pythagoras once or twice. Pythagoras appears in geometry, bearings, real-life problems (e.g. ladder against a wall), and in trigonometry (finding a side before using SOHCAHTOA). Always identify the right angle and label the hypotenuse; show your working so method marks are awarded.

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