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.
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Your hypothesis seems well supported by your data. What do you think you will look at next? Do you have another question about this? Are you going to try to answer another question about right triangles? Remember that you should be moving toward a goal of creating and investigating your own question.
ReplyDeleteDaniel this is really good keep up the good work
ReplyDelete-Daniel