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:
Tool 
Given 
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 
Everything else 
Again, if you are familiar with trigonometry, the following tools can be used with right triangles:
Tool 
Usage 
Sine 
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.

Cosine 
Tangent 
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.
While you are here..
... I have a small favor to ask. Over the years we have used advertising to support the site so it can remain free for everyone.
However, advertising revenue is falling and I have always hated the ads. So, would you go to Patreon and become a patron of the site?
When we reach the goal I will remove all advertising from the site.
It only takes a minute and any amount would be greatly appreciated.
Thank you for considering it! – John Page
Become a patron of the site at patreon.com/mathopenref
Other triangle topics
General
Perimeter / Area
Triangle types
Triangle centers
Congruence and Similarity
Solving triangles
Triangle quizzes and exercises
(C) 2011 Copyright Math Open Reference. All rights reserved
