Unexplained properties beside Law of Sine and Cosine.

[Dr.Peterson]

Is there a question here?

I don't see that you've either answered our questions, or asked one that we can answer.

 

[Larrousse]

Is there a question here?

I don't see that you've either answered our questions, or asked one that we can answer.

After all the facts shown here , what conclusions have you come up with?

 

[Dr.Peterson]

After all the facts shown here , what conclusions have you come up with?

That's an open-ended question, which isn't what we're supposed to do here. What sort of conclusions are you looking for?

Most of your statements are correct (the one about the reciprocal of the diameter is misstated), but not generally useful. Most can be derived as needed, so I wouldn't bother either memorizing them or looking them up; in particular, your formulas for the altitudes follow from Heron's formula for the area of a triangle, which is much more worth knowing. And the last formula requires knowing four facts about the triangle, rather than just three (as in the law of cosines), so it is wasteful.

In general, it's better to know a few facts with broad understanding, than to have long lists of facts that don't connect to the big picture. But you have perhaps benefited personally by doing all this work, which required you to look at the triangle from many perspectives. So the practice you got has more value than the end product. That's true of a lot of educational projects.