3D Trigonometry Worksheet

3D trigonometry at a glance

Three dimensional trigonometry involves using the trigonometry facts that we already know and applying them to 3 dimensional shapes such as cuboids and square based pyramids to work out missing angles and side lengths. 

When applying trigonometry or Pythagoras’ theorem in three dimensions, we first need to create a triangle. This might require drawing an extra straight line on the shape with lengths that we know or can calculate. Sometimes we might need to use given information on the  midpoints or ratios of side lengths. Once we have a triangle, we can apply SOHCAHTOA, the sine rule or the cosine rule. 

As with 2 dimensional shapes, we can decide which formula is the most appropriate by first determining whether the triangle has a right angle and then looking at what information we are given. If it is a right angle triangle then using Pythagoras’ theorem or the basic trigonometric ratios of sin, cos and tan would be the most appropriate. If it is not a right angle triangle then we need to use the sine rule or the cosine rule. 

 Looking forward, students can then progress to additional geometry worksheets, for example a 3D shapes worksheet or an area of a triangle worksheet.

For more teaching and learning support on Geometry our GCSE maths lessons provide step by step support for all GCSE maths concepts.