I/D #2 Unit O- How Can We Derive the Patterns of Our Special Right Triangles?

INQUIRY ACTIVITY SUMMARY

          30 60 90 Triangles

·        The first thing you want to do is cut the equilateral triangle in half. To find the degrees we know that the bottom right corner is equal to 90, to bottom left corner is equal to 60 and the top since it was split in half is 30. After this, label the sides (a, b, c) from this we learn that a=1/2 b= unknown, and c=1. To find b we use the Pythagorean Theorem.

After this you should get b to equal (√3/2).now, we multiply everything by 2. The values should equal 1n, n√3, 2n. We use N because it is a variable, that shows that the ratio can be used in other multiples of the triangle.

45 45 90 Triangles

·        For this triangle we also start by cutting it in half diagonally. The angles are much easier to find in the triangle. Label all sides a, b, & c. we should find that a=1 and b=1.

 We plug these values in the Pythagorean Theorem and find that c=√2. We multiply all these values by “N” because it is a variable and it shows that this ratio works with all multiples of this triangle. Our final ratio should be a=n b=n & c=√2

INQUIRY ACTIVITY REFLECTION

·        Something I never noticed before about special right triangles is… you can derive the ratios for these triangles by setting the sides to 1 and using the square and the equilateral triangle.

·        Being able to derive these patterns myself aids in my learning because… when I forget the ratios I can still find them by using what I learned.