My Last Post

The question that I have been investigating since my last blog is still, do all triangle angle combinations (like 30-60-90 or 20-70-90) all have the same side lengths if you change the length of the hypotenuse? I have found this data since my last post.

Angles 40-50-90:

Line AC	21	22	23	24	24	26	27	28	29	30
Line BC	16	16	17	18	19	19	20	21	22	22
Line AB	13	14	14	15	16	16	17	17	18	19

Angles 20-70-90

Line AC	21	22	23	24	25	26	27	28	29	30
Line BC	7	7	7	8	8	8	9	9	9	10
Line AB	19	20	21	22	23	24	25	26	27	28

I have also gotten the data in my last post. The conclusion that I came up with is that no matter what the angles are, the side lengths will usually be different. This is because in my previous post, Line BC and Line AB were different even though the hypotenuse was the same. The only similarity was the hypotenuse. So basically, angles make up pretty much all of your sides. If the angle is bigger, the side lengths get bigger too. The next question that I will be investigating is, are there any angle combinations (like 20-70-90) that have the same side lengths? (minus the hypotenuse). Also, another question I want to investigate is, If you give two given sides, what happens to the angles?

tables of my data

These tables represent what I have found out so far in this investigation.

Line AC	11	12	13	14	15	16	17	18	19	20
Line BC	3	4	4	4	5	5	5	6	6	6
Line AB	10	11	12	13	14	15	15	16	17	18

Line AC	21	22	23	24	25	26	27	28	29	30
Line BC	7	7	7	8	8	8	9	9	9	10
Line AB	19	20	21	22	23	24	25	26	27	28

Line AC	31	32	33	34	35	36	37	38	39	40
Line BC	10	10	11	11	11	12	12	12	13	13
Line AB	29	30	31	31	32	33	34	35	36	37

Line AC	41	42	43	44	45	46	47	48	49	50
Line BC	14	14	14	15	15	15	16	16	16	17
Line AB	38	39	40	41	42	43	44	45	46	46

 

When I went back to my question that I have been wondering about, do all triangle angle combinations (like 30-60-90 or 20-70-90) all have the same side lengths if you change the length of the hypotenuse, and I made the angles 40-50-90. I found out that, no, the side lengths are not the same length if you change the hypotenuse and the angle measures. The pattern is even different.

Here is a table to show what I mean:

Line AC	11	12	13	14	15	16	17	18	19	20
Line BC	8	9	9	10	11	12	13	13	14	15
Line AB	7	7	8	8	9	10	10	11	12	12

When the angle measures were 20-70-90, and when Line AC was 11 (Line BC:8 Line AB:10), Line AC for 40-50-90 was also 11 but Line BC was 8  and Line AB was 7. The new pattern that I found is that the numbers for Line BC would be the same twice in a row then be different three times in a row. For Line AB, I found that the numbers would be the same twice in a row but then another number twice in a row would be the same then that again. After that there would be a lone number only once then back to the numbers twice in a row. This pattern is much different than the one that I found for my original question.