Triangles are important in the real world because they are structurally stable
Even walls that are rectangular have diagonal bracing, so they also have triangular stability.
Triangles are also important in surveying …
… and in many other uses besides.
The Pythagorean Theorem goes a long way when it comes to solving right triangles, but not every triangle has a right angle.
Arbitrary tringles can be solved by using the law of sines and the law of cosines.
The law of sines says that the ratio of sines of angles and the sides opposite them are in proportion. It can be used to find an unknown side of a triangle when another side and both opposing angles are known, or to find an unknown angle when another angle and both opposing sides are known.
The law of cosines is a generalization of the Pythagorean Theorem. It can be used to find an unknown side when the other two sides and the angle between them are known, or to find an unknown angle when all three sides are known.
This simulation will allow you to see how the Law of Sines and the Law of cosines are used to solve oblique triangles.
Enter in any three elements of a triangle, including at least one side. You can enter values by using the sliders or by entering values in to entry fields. Press the “Solve” button when you have entered three values.
The simulation will show what can be done to find the other three elements, as well as draw a diagram of the triangle.
You may want to have pen or pencil, paper, and a calculator handy to work out solutions as the simulation takes you through them.
Before long, you’ll have an intuitive understanding of how and why to use the law of sines and the law of cosines!