Since the last time I blogged I was investigating questions from my teacher, now I have made up my own question....
In a right triangle, if you change the hypotenuse leg, what will happen to the longer leg and shorter leg?
This right triangle is a 10-80-90:
There is a relationship between the Longer Leg and the Short Leg and between the Longer Leg and the Hypotenuse Leg. The relationship between the Longer Leg and the Short Leg is the Longer Leg x .1763 = Short Leg. This relationship is shown in the table below. There is another relationship between the Longer Leg and the Hypotenuse Leg. The relationship is Longer Leg x 1.0154 = Hypotenuse Leg. This relationship is shown in the table below.
| Hypotenuse Leg | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| Longer Leg | .9848 | 1.9696 | 2.9544 | 3.9392 | 4.9240 | 5.9088 | 6.8936 | 7.8784 | 8.8632 | 9.8480 |
| Short Leg | .1736 | .3472 | .5209 | .6945 | .8682 | 1.0418 | 1.2155 | 1.3891 | 1.5628 | 1.7364 |
I had to take many steps to investigate this triangle. I used the website: http://www.saltire.com/applets/triangles/tri1s2a.htm to find my information. It also took me some complicated calculations to get this pattern. My next step will be to finish looking at all Right Triangles and seeing if they have a similar pattern to eachother.
You should look at Rayna's blog http://trianglesrsm.blogspot.com/, she looked at the same set of triangles and found similar patterns. I wonder if you could compare data and come up with more general rules, or if there are even any general rules.
ReplyDeleteall of your blogs are good but could u include pictures to show what your triangle you are talking about. does every triangle follow a pattern or rule it has to go by?
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