# 3D Trigonometry

A collection of videos, solutions, activities and worksheets that are suitable for GCSE Maths.

How to solve problems that involve 3D shapes using trigonometry and the Pythagoras' Theorem?

The following diagram gives an example of the projection of a line on a plane and the angle between a line and and plane. Scroll down the page for more examples and explanations on using Trigonometry and the Pythagoras' Theorem to solve 3D word problems.

GCSE Maths 3 D Trigonometry A* Question

Example:
ABCDEFG is a solid cuboid.
a) Find the length BE
b) Calculate the angle that BH makes with the plane ABFE.

IB Math Studies: 3D Trigonometry

Examples:

1. A room is in the shape of a cuboid. Its floor measures 7.2m by 9.6m and its height is 3.5m.
a) Calculate the length of AC
b) Calculate the length of AG
c) Calculate the angle that AG makes with the floor.
2. The right pyramid shown in the diagram has a square base with sides of length 40 cm. The height of the pyramid is also 40 cm.
a) Find the length of OB.
b) Find the size of angle OBP.

Trigonometry and Pythagoras in 3D Shapes
Calculating an angle between an edge and plane in a 3D shape using Pythagoras and trigonometry.

Example:
For this cuboid calculate
a) Length AG
b) Angle between AG and the plane ABCD

Angle between a line and a plane

3D Trigonometry Problem
The worked solution to a three-dimensional trigonometry problem.
A tree on the far side of a river bank is used to determine the width of the river with the help of a few right angle triangles.
Step 1: Identify the right angles in your diagram.
Step 2: Include all the measurements in your diagram.

How to do Trigonometry in Three dimensions?
3D trig Pythagoras cuboid Part 1

Example:
ABCDEFGH is a cuboid with dimensions 4m, 2m and 1.5m. X is the midpoint of the side EF. Find the lengths AC, AG and AX. Find the angles GAC and AXB.

3D Trig Pythagoras cuboid part 2.

3D Trig Pythagoras cuboid part 3.

3D Trig Pythagoras cuboid part 4.

3D Trig Pythagoras cuboid part 5.

Try the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.