Geometry/Chapter 4/Lesson 9

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Introduction[edit]

This page will teach you about special right triangles.

Special Right Triangles[edit]

30-60-90[edit]

30-60-90 triangle formula

A pattern is shown here:

Only if 30 is the vertex angle and 60 is the other angle apart from 90 and 30.
  • a=4, other leg=4√3, hypotenuse= 8
  • a=9, other leg=9√3, hypotenuse= 18
  • other leg=8√3, a=8, hypotenuse 16

..and so on and so forth. EXCEPT!

Special Cases[edit]

45-45-90[edit]

Each of these digits separated by a dash is angle degrees. The two base angles are congruently 45 while the vertex angle is 90.

So, if a= 6, then other leg is 6 and the hypotenuse 6√2... simple and easy pattern you can see here. If:

  • a= 10, other leg= 10, hypotenuse= 10√2
  • a= 13, other leg= 13, hypotenuse = 13√2
  • hypotenuse= 9√2, other leg and a= 9
  • hypotenuse= 689√2, other leg and 1= 689

..and so on and so forth. EXCEPT!

Special Cases[edit]

See also[edit]