# Why do you need to use special right triangles?

Mar 6, 2015

I've always thought of them as providing a collection of standard, known results.

In learning or teaching any application (physics, engineering, geometry, calculus, whatever) we can assume that students who know trigonometry can understand an example that uses angles of ${30}^{\circ}$, ${60}^{\circ}$, or ${45}^{\circ}$ (pi/6, $\frac{\pi}{3}$, or pi/4).

Apr 12, 2015

In general, there are 2 types of special right triangles.
Type 1. Right triangle that is half of a equilateral triangle. Its angle measures are: 30 , 60 and 90 deg.
Type 2. Right triangle that has its side measures in the ratio 3:4:5.
Use of special Right triangles.
In the old time, people used special right triangle, with side ratio 3:4:5, to figure out a right angle on the field. They can also find the measures of the 3 sides of a right triangle, knowing the ratio and one of the 3 sides.