Pythagoras and Trigonometry in 3D

Pythagoras and Trigonometry in 3D: Exam Questions

These presentation show students how to solve real IGCSE exam questions on Pythagoras’ Theorem and trigonometry in 3D, including finding the angle between a line and a plane.

Each question is worked through one step at a time. Students first see a large, clear 3D diagram. Then the right-angled triangle needed for that step is shaded inside the shape. Next, that triangle is drawn out in 2D. Only then does the working appear, one line at a time, with a short explanation of each step.
In this lesson students apply Pythagoras’ Theorem and trigonometry to problems in three dimensions. They learn to spot the right-angled triangles hidden inside 3-D shapes such as cuboids, prisms and pyramids, and to draw each triangle in 2-D before using Pythagoras or SOH CAH TOA. Students then find the angle between a line and a plane by dropping a perpendicular to the plane and using the projection (the “shadow”) of the line. The lesson builds from 2-D right-angled triangles, to diagonals in 3-D shapes, to multi-step IGCSE exam questions — including the June 2019 cube question and a pyramid question where the height must first be found from the total surface area.