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.
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These are very interesting patterns. I like how you were able to be specific about the numbers and to generalize the pattern by using algebra. I think that your new questions will lead you in a good direction. Let me know if you need any guidance.
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