Trigonometry - 3D problems

A complete lesson on using SOHCAHTOA and Pythagoras’ theorem with problems in three dimensions.

Activities included:

Starter:
A set of recap questions on basic SOHCAHTOA and Pythagoras.

Main:

• Examples and questions to dscuss, on visualising distances and angles within cuboids and triangular prisms, and understanding the wording of exam questions on this topic.
• Examples and quick questions for pupils to try, on finding the angle of a space diagonal.
• A worksheet, in three sections (I print this, including the starter, two per page, two sided so that you have a single page handout), with a progression in difficulty. Starts with finding the space diagonal of a cuboid, where the triangle pupils will need to use has been drawn already. The second section looks at angles in a triangular prism, and pupils will need to draw the relevant triangles themselves. The third section has exam-style questions, where pupils will need to identify the correct angle by interpreting the wording of the question. (eg “find the angle between the diagonal AE and the plane ABCD”).
• An extension task looking at the great pyramid of Giza.

Plenary:
A final question to add a bit more depth, looking at the most steep and least steep angles up a ramp.

Printable worksheets and worked answers included.

Please review if you buy as any feedback is appreciated!