Trigonometry

Study of triangles and trigonometric functions including sine, cosine, and tangent.

Understanding Angles and TrianglesSine, Cosine, and Tangent FunctionsThe Unit Circle and Radian Measure
Trigonometric Identities and FormulasSolving TrianglesGraphs of Trigonometric Functions
Measuring Heights and DistancesTrigonometry in Engineering and DesignNavigation and GPS
Memorizing Trigonometric ValuesSolving Word Problems with DiagramsChecking Your Work with Inverse Functions
Understanding Angles...Sine, Cosine, and Ta...The Unit Circle and ...Trigonometric Identi...Solving TrianglesGraphs of Trigonomet...Measuring Heights an...Trigonometry in Engi...Navigation and GPSMemorizing Trigonome...Solving Word Problem...Checking Your Work w...
Advanced Topics

Solving Triangles

Finding Missing Pieces

To "solve" a triangle means to find any unknown sides or angles using what you know. You can use:

  • The Pythagorean theorem for right triangles: \( a^2 + b^2 = c^2 \)
  • Trig functions (sine, cosine, tangent) for right triangles
  • Law of Sines and Law of Cosines for any triangle

These methods unlock the mystery of any triangle!

Examples

  • Given a right triangle with hypotenuse 10 and one side 6, use the Pythagorean theorem to find the other side: \(6^2 + b^2 = 10^2\).

  • If you know two angles and one side of a triangle, you can use the Law of Sines to find another side.

In a Nutshell

Use trigonometric tools to find unknown sides or angles in triangles.

Next
Graphs of Trigonometric Functions