Daniel is still the man. iBall.

Question: If you change a side of a right triangle, does the angle change and if so how much?

If you have a right triangle and you change a side < A or < B will change depending on which side you change. If you change side BC, angle B will change and if side AC, angle A will change. First before I move anything the sides are 9, 9, and 12.728 and the angles are 45, 45, and 90 degrees. Here is an example of the data that I found.

I changed side BC
1. < A 37.88, < B 52.13, < C is always 90, side AC=9, BC=7, AB=11.402
When I changed side BC angle A got smaller and angle B got bigger as you can see in the data above.
So when I changed one side that angles change except angle C. I am going to show you another example but I am going to change side AC.

2. < A 60.95, < B 29.05, < C 90, side AC=5, BC=9, AB=10.296
I changed side AC and angle A got bigger and angle B got smaller and angle C stays the same. The angles change when I change a side. When there is a difference of the sides by one the angle are a difference of 7 degrees. The two sides of the data are 9 and 5, and the difference between the angles is about 32 degrees.

Daniel is the man.

These are the questions you asked. Can you predict how close the angles will be? If you know the difference between the sides, can you predict the angles?

The last few days this is what I did to investigate on this question. I have noticed that when the two side lengths are within 2 the degrees are within 6 degrees for an example in my data the sides lengths were 13.5 and 12.4 and the two degrees were 48 and 42. If I were to know the sides I probably would not be able to exactly know the angles but I would be really close, as I found in my data. The data I found tells me a lot about the different angles and lengths.

I am going to show you an example of data about the sides and the angles:

Side 1 17.1, Side 2 18.6, Hyp. 25.25, < A 43 degrees, < B 47 degrees, < C 90 degrees

The two sides are close and therefore that makes the angles close as you can see from the data.

Now here is some data that has two lengths in a difference of 5.
Side 1 16.1, Side 2 10.9, Hyp. 19.41, < A 56 degrees, < B 34 degrees, < C 90 degrees

There is only a difference of 5 and there is a difference of 22 degrees. My assumption is that if there is a difference 1 of the lengths there is a difference of 4 degrees. For every difference of lengths there is a difference of 4 degrees.

If you know the side lengths of a right triangle, can you predict

Hypothesis: My hypothesis is that if you know the side lengths of a triangle you can predict the angles because of the Pythagorean theorm.

Investigation: The question that I am investigating is "If you know the side lengths of a right triangle, can you predict what the angles will be?". That is the only question that I am investigating.

What I did to investigate this question is going on a website that my teacher suggested for and I used it. I found data on that question. I had to find the following data of sides A and B, the angles would showed up every time we changed the sides. Then I had to write that data down, the angles and the sides. The data was my proof on the question that I had.

The things that I have found so far are the sides and angles. Here are some actual data.

Side 1 Side 2 hyp. < A < B < C
18 24 30 37 degrees 53 degrees 90 degrees

That was one set of my data. I have also found a pattern, when side 1 and side 2 are two close numbers the two angles are close here is one example from my data table.

13.5 12.4 18.28 48 degrees 42 degrees 90 degrees

The two sides 13.5 and 12.4 are two very close numbers and the two angles are close. They are 48 and 42. That is the pattern I have found for all of the data I took down from the website.