Applying Pythagoras’ theory and trigonometry to 3D shapes

Task goals

• Find face diagonals of rectangular faces in 3D shapes using Pythagoras' theorem.
• Calculate space diagonals of cuboids using a two-step method combining Pythagoras applications.
• Use trigonometric ratios (sine, cosine, tangent) to find heights or angles when given a sloping line and one other measurement.
• Solve multi-step 3D problems that require both Pythagoras' theorem and trigonometry to reach the final answer.
• Identify which right triangle to use in a 3D context and determine whether the angle is measured from the base or vertical.
• Justify solutions using both exact values and decimal approximations, recognising when early rounding affects the final answer.