# What are the Special Right Triangles?

Dec 7, 2014

Special Right Triangles

1. ${30}^{\circ}$-${60}^{\circ}$-${90}^{\circ}$ Triangles whose sides have the ratio $1 : \sqrt{3} : 2$

2. ${45}^{\circ}$-${45}^{\circ}$-${90}^{\circ}$ Triangles whose sides have the ratio $1 : 1 : \sqrt{2}$

These are useful since they allow us to find the values of trigonometric functions of multiples of ${30}^{\circ}$ and ${45}^{\circ}$.

Apr 13, 2015

There are 2 types of special right triangles.
Type 1. Triangle that is half of a equilateral triangle. Its 3 angle measures are: 30, 60 and 90 deg. Its side measures are : a, a/2; and (a*sqr.3)/2.
Type 2. Triangle that has its side measures in the ratio of 3:4:5. The proof is given by the Pythagor theorem: c^2 = b^2 + a^2.
Use of special right triangles.
In the old time, people use the special right triangles with sides ratio 3:4:5 to figure out, in the field, a right angle or a rectangular, or square, shape.
Now, students just use the properties of special right triangle to find, by computing, the unknown sides or angles.