I/D 2: Unit O-How can we derive the patterns for our special right triangles?

30-60-90

We label all the sides of the triangle 1. We then cut the triangle in half and notice that since all the angles are 60 the angle at the top will be cut in half and made into 30 degrees after this we can label the triangle sides "a", "b" and "c". The horizontal line was one and was cut in half so we know that the length of the new side is 1/2. We see that we are missing side "b" so we use the pythagorean theorem to solve for the missing angle. when we do a^2+b^2=c^2 we get "b" to equal radical (3/2) we know that we can't have any fractions so we multiply every side by two and get a=1 b=radical 3 c=2. we then can add the variable "n" to show that this pattern can be applied to another function.

45-45-90

i started by cutting the square diagonally. We know that each angle in the square is 90 degrees so by cutting it in half we know that half of 90 is 45 degrees. We also know that the two angles that are not the 90 degree angle are the same measurement. we are given 1 as the side length to all the sides and we label the sides "a", "b" and "c" we are missing "c" so we use the pythagorean theorem to find "c" we end up getting "c" to equal the square root of 2. We know that we can add the variable "n" to show that this also is a pattern that can be applied to another function.