G S Rehill's Interactive Maths Software Series - "Building a Strong Foundation in Mathematics" from mathsteacher.com.au.

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Year 10 Interactive Maths - Second Edition


Three-Dimensional Problems

To solve a three-dimensional problem, it is important to be able to visualise right triangles contained in a diagram.  Then redraw the right triangles in two dimensions and use an appropriate trigonometric ratio and/or apply Pythagoras' Theorem to obtain the answer.


Example 22

Find the angle between the body diagonal and the base of a cube of side-length 5 cm.

Solution:

By Pythagoras' Theorem and triangle ACD,

Taking the square root of both sides gives



So, the angle between the body diagonal and the base of the cube is 35º16/.


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