Final Blog Entry!!:

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.

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 1 .364 1.064 70
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 1 .532 1.133 62
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 1 .649 1.192 57
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???

Third Blog Entry

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.

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.

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.