Solving the Triangle
What does 'solving the triangle' mean?
It means that if we are given some facts about a triangle, we can find some or all of the rest.
For example, if we know two sides of a right triangle we can find (or 'solve for') the third side using Pythagoras' Theorem.
To completely solve a triangle it usually means finding everything about it - all three sides and all three angles. But often we are just interested in
one unknown aspect of the triangle.
Tools for solving triangles
If you are familiar with trigonometry, the following tools can be used with any triangle:
||You can find
|Law of Cosines
||Two sides and the angle between them
||The third side
|Law of Sines
||One side and its opposite angle, and one other item
Again, if you are familiar with trigonometry, the following tools can be used with right triangles:
These trigonometry functions relate an angle and two other sides. If you know two of the three, you can find the other.
It is beyond the scope of the this volume on Geometry to define them here. See the Trigonometry Overview for a brief description.
The tools listed above can be used in any combination. There is no 'right way' of solving a triangle (or any other geometric problem).
Just as in woodworking, you can use the tools in many ways and in many sequences.
Think about what you have been given to start, and find tools that lead you in the direction you want to go.
Related triangle topics
Perimeter / Area
Congruence and Similarity
Triangle quizzes and exercises
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