Right triangles & trigonometry

This course is a part of Mathematics II, a 14-course Topic series from Khan Academy.

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.

This course contains 9 segments:

Pythagorean theorem

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.

Pythagorean theorem proofs

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.

Special right triangles

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).

Introduction to the trigonometric ratios

Learn what sine, cosine, and tangent are.

Solving for a side in a right triangle using the trigonometric ratios

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

Solving for an angle in a right triangle using the trigonometric ratios

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

Modeling with right triangles

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

Trigonometric ratios & similarity

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

Sine & cosine of complementary angles

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°.