When investigating if it is possible to figure out the angles of a triangle by knowing the side lengths, found something that changed my idea. The numbers 6-8-10 are a pythagorean triple. the numbers 24-18-30 are all multiples of 3, 6 multiplied by 3 equals 18, 8 multiplied by 3 equals 24 and 10 multiplied by 3 equals 30. Which is a pattern I found interesting. Another thing that I noticed s that when I used 6-8-10 and
24-18-30 they had the same angle measurements. If there is a specific way to figure out how to find the angles of a triangle when you know their side lengths, how can you find thatwhen you can have different side lengths give you the same angle measurement?I think that there are other parts of triangles that would help us determine the angles in a triangle, when you only know the side lengths of that triangle. In geometry for the triangle unit we have only been working with the angles and sides of a triangle but there has to be many other parts of a triangle that could help us figure out the measurements of the angles. Based on the information we have been learning we know how to find the angles of a triangle when there are two triangles involved and an angle is already given, which does not seem to be enough to help us figure out the measurements of the angles in a triangle.
You are right that there are many triangles with the same angles and different side lengths. They are called similar triangles, and their side lengths are proportional. One way to think about this issue is to consider the side lengths of triangles in terms of rations. For example, what is the ratio of one side length to another, or what is the ration of one side length to the hypotenuse. This could help you deal with the fact that the same angles can produce many different triangles.
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