Blog Entry #5:
Ok so the past question I have been investigating is if there are any other angle combinations for right triangle that could help you find the missing leg and hypotenuse of the triangle, besides the ones we have been working on in class. The ones I already knew was the 45-45 90 or the 30-60-90. In my first blog entry I tried to increase the measure of one side each time, I drew a different triangle each time and that was where I hit trouble because my data was confusing and incorrect. So my teacher told me to try and look for different patterns within the side lengths of the triangle. Each time I had a triangle with one right angle and two other angles that added up to 90 degrees; these angle measures were my choice. After doing this a few times I realized that I wasn’t going to find any other angle combinations besides the two I knew, and the side lengths were decimals and not integers like I’d hoped. So I continued my investigation looking at patterns with in the side lengths of a right triangle.
Each time I made a different sized right angle with 3 constant angle measures and a long leg with an increasing size of one inch, starting at one inch. In my four different data tables I noticed that the lengths of the short leg could determine the length of the long leg depending on the size. For example a 20-70-90 triangle has a long leg length of 4, to find the short leg I could take the measure of the original sized triangle and multiply it by the size of the long leg. This would help me find the size of another triangle the same size but with different long leg length. My information to find the long legs length could also be used to find the hypotenuse. If this is confusing look at my ld blogs and compare the patterns, see if you can spot them! J
In conclusion I think that there is no other angle combination to determine the lengths in the sides of triangles, because you can find a pattern using the side lengths. The only requirements is a constant and a coefficient. There needs to be something that stays the same each time and some number that increase/decreases each time. If I was to create another question to help continue my research I would want to know can you find the angle measures of a triangle by knowing two side lengths? This could help me to try and find another angle combination whos lengths were not integers and instead whole numbers like the original two combinations I learned in class.
Wednesday, April 8, 2009
Monday, April 6, 2009
Bog Entry #4
Blog Entry #4: Now I’m trying to see if I can find any other patterns with other right triangle combinations. The following triangle has angle measures of 90-70-20, the one after is going to have angle measures of 90-28-62.
Side AC
Side BC Side AB
2 .728 2.128 70
3 1.092 3.193 70
4 1.455 4.256 70
5 1.819 5.320 70
6 2.183 6.385 70
7 2.547 7.449 70
8 2.912 8.513 70
9 3.275 9.577 70
10 3.639 10.641 70
This table shows the change in the sides of a triangle with 90-62-28. I made this triangle to have sides with out angle measures that were multiples of ten and five. The next triangle will have odd angle measures.
Side AC
Side BC Side AB
2 1.063 2.265 62
3 1.595 3.397 62
4 2.126 4.530 62
5 2.658 5.662 62
6 3.190 6.795 62
7 3.721 7.927 62
8 4.253 9.060 62
9 4.785 10.193 62
10 5.317 11.325 62
Side AC
Side BC Side AB
2 1.298 2.384 57
3 1.948 3.577 57
4 2.597 4.769 57
5 3.247 5.961 57
6 3.896 7.154 57
7 4.545 8.346 57
8 5.195 9.538 57
9 5.844 10.731 57
10 6.494 11.923 57
After looking at both triangles and there lengths I have come to the conclusion that all triangles have an equation to find there hypotenuse and length of the short leg. The equation for the first triangle is .532n=length of the short leg and the equation to find the length of the hypotenuse is 1.133m=hypotenuse.
The second triangle’s equation is .649n=length of short side the other one is 1.192m=hypotenuse. This shows me that there can be any angle combinations. The combinations may have decimal points, but they still can be useful to find the sides of triangles.
I have no idea on what my next question should be can you help???
Side AC
Side BC Side AB
2 .728 2.128 70
3 1.092 3.193 70
4 1.455 4.256 70
5 1.819 5.320 70
6 2.183 6.385 70
7 2.547 7.449 70
8 2.912 8.513 70
9 3.275 9.577 70
10 3.639 10.641 70
This table shows the change in the sides of a triangle with 90-62-28. I made this triangle to have sides with out angle measures that were multiples of ten and five. The next triangle will have odd angle measures.
Side AC
Side BC Side AB
2 1.063 2.265 62
3 1.595 3.397 62
4 2.126 4.530 62
5 2.658 5.662 62
6 3.190 6.795 62
7 3.721 7.927 62
8 4.253 9.060 62
9 4.785 10.193 62
10 5.317 11.325 62
Side AC
Side BC Side AB
2 1.298 2.384 57
3 1.948 3.577 57
4 2.597 4.769 57
5 3.247 5.961 57
6 3.896 7.154 57
7 4.545 8.346 57
8 5.195 9.538 57
9 5.844 10.731 57
10 6.494 11.923 57
After looking at both triangles and there lengths I have come to the conclusion that all triangles have an equation to find there hypotenuse and length of the short leg. The equation for the first triangle is .532n=length of the short leg and the equation to find the length of the hypotenuse is 1.133m=hypotenuse.
The second triangle’s equation is .649n=length of short side the other one is 1.192m=hypotenuse. This shows me that there can be any angle combinations. The combinations may have decimal points, but they still can be useful to find the sides of triangles.
I have no idea on what my next question should be can you help???
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