Geometry/Chapter 4/Lesson 9

Introduction

This page will teach you about special right triangles.

Special Right Triangles

30-60-90

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!

45-45-90

45-45-90 triangles

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!

See also

• https://www.khanacademy.org/math/geometry/hs-geo-trig/hs-geo-special-right-triangles/v/45-45-90-triangles