The Cosine Law - Solving for Angles
We have been working on applying the cosine law to solve for unknowns in non-right triangles. The last video lesson and blog discussed how to apply the cosine law to solve for unknown side lengths. We know that to do this we need to be given any two sides and a contained angle between them.
To solve for an unknown angle while using the cosine law we need to be given all three sides.
The following is a example of the various ways we can arrange the cosine law in order to solve for each unknown angle of ∆ABC:
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| The Cosine Law - Solving for Angles. Created by Mike Studenny. |
The important pieces to notice when using the cosine law and solving for angles can be summaries into a few key points:
- The equation is simply a rearranged version of the cosine law used to solve for sides.
- The equation still matches the unknown value on the left of the equation to it's partner on the far right (i.e., unknown angle A matches to given side a.)
- The equation contains the two other side lengths than the matching one.
- These two other side lengths appear twice once in the numerator and once in the denominator.
The video lesson that corresponds to this blog post explains how to apply the equation to isolate for the unknown angle. If you have a strong understanding of the primary trigonometric ratios and how to isolate for unknowns using them this math should not be too difficult. Generally, the hard part is developing the equations correctly.
Follow the link below to access the video lesson:
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