Blog Entry #3:
The question I have been looking at since my last blog entry is if there are any patterns in the changes in side, with a 90-54-36 triangle. I was looking for any patterns in within the increasing side lengths of the short and long leg. The point of this was to know that if I knew the length of one leg and the angles could I predict the lengths of the other leg and the hypotenuse.
Side AC
Side BC Side AB < ABC
1 inch .727 1.236 54
2 inches 1.453 2.472 54
3 inches 2.179 3.708 54
4 inches 2.906 4.944 54
5 inches 3.632 6.180 54
6 inches 4.359 7.416 54
7 inches 5.085 8.652 54
8 inches 5.812 9.888 54
9 inches 6.538 11.124 54
10 inches 7.265 12.361 54
After looking at the table I noticed that there in fact was a pattern. The pattern was between sides BC, the first length was .727 inches, the second length of the next triangle was twice that amount. So was the third, fourth and excreta. With this I could make an equation. Side BC has a variable and the constant is .727, together the coefficient is .727n= length of the short side.
I can do the same thing with side AB where the variable is “m” and the constant is 1.236, all together the coefficient is 1.236m= length of the hypotenuse.
These equations help me find a triangle’s lengths of all the sides. Next I will try to find these same patterns with other triangles with different angle measures of 90-70-20.
Tuesday, March 31, 2009
Saturday, March 28, 2009
BLOG ENTRY #2
My last blog had a table with triangle sides. All of the side lengths of the longer sides were numbers with decimals. I tried to see if i could find any three combination of angles to make a triangle with side lengths that are integers. After playing around with triangles i found that there is no combination of angle measures that have all whole number sides.When i did some work i had a triangle with a 90-80-20 angle measures and the sides cam out to be .75-1.5-1.75. This information showed me that there seems to be no integer lengths in the sides of right triangle besides the two that everyone already knows. The question i now have is if there can be any angle cominations that have easy to use decimals, that could be a correct combination. My plan to find this information out is to ask my techer Ms.Sheppard-Brick that, but first im goin to continue my search to find angle combinations that work and have deciamls.
My last blog had a table with triangle sides. All of the side lengths of the longer sides were numbers with decimals. I tried to see if i could find any three combination of angles to make a triangle with side lengths that are integers. After playing around with triangles i found that there is no combination of angle measures that have all whole number sides.When i did some work i had a triangle with a 90-80-20 angle measures and the sides cam out to be .75-1.5-1.75. This information showed me that there seems to be no integer lengths in the sides of right triangle besides the two that everyone already knows. The question i now have is if there can be any angle cominations that have easy to use decimals, that could be a correct combination. My plan to find this information out is to ask my techer Ms.Sheppard-Brick that, but first im goin to continue my search to find angle combinations that work and have deciamls.
Wednesday, March 25, 2009
Question: Are there any other angle combination besides 45-45-90 and 30-60-90?
Blog entry #1
In my geometry class I was asked the question, if there are any other angle combinations besides 45-45-90 and 30-60-90 that show similar patterns? So I started to collect some data to try and find any similarities between the side lengths of triangle. First I started with a triangle with a short leg length of 1 inch, then I choose to have my angles of the triangle be 90-50-40, the triangles name is ABC. I made about six triangles then each time I increased the measure of side AB (short leg) which is one inch long. Each time I drew a new triangle I increased the size by one inch, then I measured the longer leg and hypotenuse. After creating about six triangles I noticed a pattern. The pattern was that the longer leg would be a half a inch bigger than the shorter leg, and the hypotenuse would be a half an inch greater than the longer leg. In other words the length of the hypotenuse is an inch greater than the short leg. Down bellow is a table of my results.
| Short Leg: | Longer leg: | Hypotenuse: |
| 1 inch | 1.5 inches | 2 inches |
| 2 inches | 2.5 inches | 3 inches |
| 4 inches | 4.5 inches | 5 inches |
| 5 inches | 5.5 inches | 6 inches |
| 6 inches | 6.5 inches | 7 inches |
After finding this data I don’t really think it can help me to find other angle combination because the longer legs are not integers. With this information I think I need to change my selected angle choices of size.
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