Know, derive and apply Pythagoras’ theorem \(a^2 + b^2 = c^2\) to find lengths in right-angled triangles in 2D figures.

Apply Pythagoras’ theorem in more complex figures, including 3D figures.

Know and apply the trigonometric ratios, \(\sin{\theta}\), \(\cos{\theta}\) and \(\tan{\theta}\) and apply them to find angles and lengths in right-angled triangles in 2D figures.

[see also Similar shapes, 9.04c]

Apply the trigonometry of right-angled triangles in more complex figures, including 3D figures.

Know the exact values of \(\sin{\theta}\) and \(\cos{\theta}\) for \(\theta = 0°, 30°, 45° , 60°, 90° \)

Know the exact value of \(\tan{\theta}\) for \(\theta = 0°, 30°, 45°, 60° \)

Know and apply the sine rule,

\(\dfrac{a}{\sin{A}} = \dfrac{b}{\sin{B}} = \dfrac{c}{\sin{C}} \)

to find lengths and angles.

Know and apply the cosine rule,

\(a^2 = b^2 + c^2 - 2bc\cos{A} \)

to find lengths and angles.