# Why 90 degree triangles

1. Aug 8, 2012

### Avichal

Why do we study so much about right triangles like trigonometry. We could define sin and cos like functions in a 70 degree triangle too.
I also know right triangle is something special but i dont know what is it. Also why wont trigonometry on other type of triangles be not so good

2. Aug 8, 2012

### arildno

Because right-angled triangles are simplest to start out with.
Furthermore, trigonometry based on that is sufficient to handle all questions you would like to ask non-right-angled triangles, as well. Thus, developing other types of plane trigonometry is unnecessary and a waste of time.

3. Aug 8, 2012

### klausas

If you find yourself working with a lot of 70 degree triangles, or any other number of degrees for that matter, feel free to make a trig table based on that if you feel it will save you time.

Right triangles are preferable as the basis for trigonometry because any other triangle can be cut into two right triangles, by drawing a line through one vertex perpendicular to its opposite side. While you could, in this day and age of analytic geometry, draw a 70 degree angled line just as well as a perpendicular, the two triangles you got from that would have one with a 70 degree angle and the other with a 110 degree angle. So, you would need two trig tables to sort it all out (or a messy set of successive approximations).

Also, when you get to unit circle trig (if you haven't already), the right triangle definition correlates with the coordinates of a point on a grid in a way that is very neat and easy to see and use. You could come up with a formula based on other angles, but it would be much messier and harder to use.

4. Aug 8, 2012

### mathwonk

sin and cos have not so much to do with triangles, they are the coordinates of points on the circle. the right triangles come in because the coordinate axes are perpendicular to each other.

The reason we use perpendicular axes, or right triangle trig, is the pythagorean theorem. The pythagorean theorem for other triangles is called the law of cosines and is more complicated.