# Right triangles & trigonometry

Contents

Triangles are not always right (although they are never wrong), but when they are it opens up an exciting world of possibilities. Not only are right triangles cool in their own right (pun intended), they are the basis of very important ideas in analytic geometry (the distance between two points in space) and trigonometry.

See how you score on these 18 practice questions

Named after the Greek philosopher who lived nearly 2600 years ago, the Pythagorean theorem is as good as math theorems get (Pythagoras also started a religious movement). It's simple. It's beautiful. It's powerful.
In this tutorial, we will cover what it is and how it can be used. We have another tutorial that gives you as many proofs of it as you might need.

The Pythagorean theorem is one of the most famous ideas in all of mathematics. This tutorial proves it. Then proves it again... and again... and again. More than just satisfying any skepticism of whether the Pythagorean theorem is really true (only one proof would be sufficient for that), it will hopefully open your mind to new and beautiful ways to prove something very powerful.

We hate to pick favorites, but there really are certain right triangles that are more special than others. In this tutorial, we pick them out, show why they're special, and prove it! These include 30-60-90 and 45-45-90 triangles (the numbers refer to the measure of the angles in the triangle).

Learn how to find a side length in a right triangle when given one side length and one acute angle.

Learn how to find an acute angle in a right triangle when given two side lengths.

Solve real-world problems that can be modeled by right triangles, using trigonometry.

Learn how the trigonometric ratios are derived from triangle similarity considerations.

Learn about the relationship between the sine of an angle and the cosine of its complementary angle, which is the angle that completes to 90°.

Learn about the Law of sines and how to use it in order to find missing side lengths and angles in general triangles.

Learn about the Law of cosines and how to use it in order to find missing side lengths and angles in general triangles.

Use the power of trigonometry in order to solve various problems that involve triangles.