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.
It seems like what you were doing here was keeping the angles the same and changing line BC by 1 each time. I suspect that the actually numbers you got were decimal values because the numbers that you have listed don't satisfy the Pythagorean theorem. I wonder if you would find more interesting or more precise patterns if you included the decimals. I know that other people have. You might want to check out Jahneice's blog at http://triangles-jng.blogspot.com/ or Rayna's blog at http://trianglesrsm.blogspot.com/
ReplyDeleteWow Amy i really like the patterns that you collected. It really helps me to understand your investigation a little bit more.
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ReplyDeleteYour data is well writen. You did a good job showing the relationship and I think it is of one angle combination. You asked a great question "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" that you actually answered. You did a good job investigating...
ReplyDeletethis is good i like patterns you collected but compared to mine the data is different from what i recieved. maybe you should recheck and make sure your data is correct.
ReplyDeleteYour investigation is great but you should try to put up a pic. of a triangle and you should mention the Pythagorean Therom... You did a good job showing all the combiniations. You should come up with some questions because they could the people who are viewing ur blog. Other than that the data chart is great!!!!
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