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Geometry & Trigonometry

Pythagoras & Right-Angled Trigonometry

Connect square areas to Pythagoras’ theorem and select SOH CAH TOA to solve right-angled triangles.

Curriculum rangeYears 8–11

a = 3, b = 4, c = 5

a^2 + b^2 = c^2

9 + 16 = 25

✓ The square on the hypotenuse (green) has the same area as the two smaller squares combined.

Learning notes

Pythagoras & Right-Angled Trigonometry essentials

Keep these rules beside you while you explore and practise.

In a right-angled triangle, the hypotenuse is opposite the right angle and is always the longest side.

a^2+b^2=c^2

Use addition to find the hypotenuse and subtraction to find a shorter side.

\sin\theta=\dfrac{O}{H}\qquad\cos\theta=\dfrac{A}{H}\qquad\tan\theta=\dfrac{O}{A}

Use the appropriate inverse function after forming the ratio.

\theta=\sin^{-1}\!\left(\dfrac{O}{H}\right)

💡Before calculating: label O, A and H relative to the marked angle—not relative to the way the triangle is drawn.