Special Right Triangles
Topic Index | Algebra2/Trig Index | Regents Exam Prep Center


There are two "special" right triangles with which you need to be familiar;  the 45- 45- 90 triangle and the 30- 60- 90 triangle.  The "special" nature of these triangles is their ability to yield exact answers instead of decimal approximations when dealing with trigonometric functions.

These triangles will be used continually throughout your studies of mathematics and are well worth your time and study. 

The most powerful method of working with these triangles is to work directly with the triangles themselves.  By remembering the "relationships" in these triangles, you will have the power to apply any of the six trigonometric functions in any situation.

Some people find charts helpful for remembering the trigonometric values of 30, 45, and 60.  Unfortunately, memorizing charts of information often gives you a limited understanding of the concepts at hand.  For example, if a chart is limited to only a few of the trigonometric functions, such as the charts seen below, your "power" to solve a multitude of problems is also limited.

  30 45 60
sin
cos

This chart shows the values with
 rationalized denominators.

  30 45 60
sin
cos

This chart shows a "trick" for remembering the values.  Notice the row for sin shows 1, 2, 3 under the radicals, while the row for cos shows 3, 2, 1 under the radicals.

 


Let's move on to studying the triangles themselves.