Sinus: Construction of Triangle (Triangles in books are sometimes only indicated with 2 lines....)

[I'mLearning]

Here is a simple question:


Triangles in books are sometimes only indicated with 2 lines.
If the sine is to be used, there are several possibilities for how the triangle can look (see image).

Do I understand it correctly that the placement of the 3rd side is not important for considerations with the sine?
Or do I fail to understand?

 

[stapel]

Here is a simple question:

View attachment 36959
Triangles in books are sometimes only indicated with 2 lines.

If there are only two lines extending from the vertex of the angle, then all they've drawn is the angle; they haven't actually drawn a triangle. (And, for working with angle measures, there is no need for a triangle; the angle measure itself is sufficient.)

If the sine is to be used, there are several possibilities for how the triangle can look (see image).

Do I understand it correctly that the placement of the 3rd side is not important for considerations with the sine?
Or do I fail to understand?

If all you're needing is the sine of the indicated angle then, no, you don't actually need a triangle. The angle itself, together with its measure, is sufficient.

 

[I'mLearning]

Oh, dear, are you all smart!
Thanks a lot!

 

[Dr.Peterson]

Here is a simple question:

View attachment 36959
Triangles in books are sometimes only indicated with 2 lines.
If the sine is to be used, there are several possibilities for how the triangle can look (see image).

Do I understand it correctly that the placement of the 3rd side is not important for considerations with the sine?
Or do I fail to understand?

To put the answer differently, the sine is a function of the angle alone, which can be defined in terms of any right triangle with that angle. Both of your triangles work; they are similar, so all ratios of sides are the same in both triangles. Similarly (no pun intended), you could make your figure any size, and you will get the same ratios.

And this is why a calculator (or in the old days, a table) can give you the sine of an angle, without needing a specific triangle.

 

[I'mLearning]

I understand!
Thank you.