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.

So far...

When I went back to one of the websites I had, I decided to put in side lengths over 10. When I did this, I noticed that when you get to the length of the hypotenuse being 17, the second longest side turned out to be two less than the side of the hypotenuse. For example, if the hypotenuse was 17, the second longest side would be 15. This only starts when I got to the hypotenuse being 17. 16 and down were all one apart. Also, for the shortest side, for three numbers in a row (for the hypotenuse side) the shortest side is the same number. for example, if the hypotenuse of three triangles was 12, 13, and 14, the shortest side would be 4. When I got to side lengths 33 and 34 for the hypotenuse, the longest side for both was 31 and the shortest side for both was 11. From then on, the second longest side is three numbers smaller instead of the starting 1. When I got to 49 and 50 being the length of the hypotenuse, the longest side were the same (46 and 46), but the shortest side were different (16 and 17).


A question that I have been wondering about is, 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?

What I've found out so far

I used this website to help me further my investigation. http://www.saltire.com/applets/triangles/tri1s2a.htm On this website, I can put in any side lengths and any 2 angles (I chose 20 degrees and 70 degrees.) when I made the side either 3, 6, or 9, the third angle wasnt exactly 90 degrees, (it was actually 89 degrees) as any other side length is 90 degrees. So far, the pattern I found is that the hypotenuse of the triangle is one more than the second longest side.

What I will be investigating

Question: We have discovered that there are patterns that appear in the lengths of right triangles with the angles 30-60-90 and 45-45-90. Are there any other any other angle combinations that show similar patterns?

I am going to see if a triangle with the angles, 20-70-90, is another one of these combinations. So far, I have found out that a triangle with angles, 20-70-90's shortest side doubles as its hypotenuse increases by one. To continue my investigation, I will be going to some given sites and try out some triangles with angles measures, 20-70-90 and change side lengths to see how it will affect the triangle.




DATA:

Line AC: 1 2 3 4 5 6 7 8 9 10
Line AB: .34 .68 1.02 1.36 1.71 2.05 2.39 2.73 3.07 3.42
Line BC: .93 1.87 2.81 3.75 4.69 5.63 6.57 7.51 8.45 9.39