I/D2: Unit O Concepts 7-8 - How can we derive the patterns for our special right triangles?

INQUIRY ACTIVITY SUMMARY

1.Cutting the 30-60-90 triangle in half gives us the 30 degree angle measurement since 60 divided by 2 is 30. To get the height note that we know what the hypotenuse is 1 since each side is 1 knowing it is an equilateral triangle and the base is 1/2 since half of one side is 1/2 and we need to find height so use the Pythagorean Theorem and you end up with rad3/2. To translate each value into normal values (without fractions) simply multiply each value by 2 so you end up with the height as rad3, the base as 1 and the hypotenuse as 2. Using n means we know each side shares the same pattern for the triangle. 

2. The 45-45-90 triangle is taken from a square and cut diagonally to get the 45 degree measurements from the triangle. 90 degrees cut in half is 45. To get the  hypotenuse you use the Pythagorean theorem and plug in 1 for the adjacent and opposite side since we know each side is labeled with 1 so we solve for c. we end up with rad2 for the hypotenuse. Using "n" means we use this variable to note that the relationship of each side is equal. 

INQUIRY ACTIVITY REFLECTION

“Something I never noticed before about special right triangles is…” Something I never noticed before about special right triangles is they each have rules that contain patterns each time you solve one!

“Being able to derive these patterns myself aids in my learning because…” Being able to derive these patterns myself aids in my learning because it gives me a greater understanding of the rules for special right triangles and understand where the constant n comes from and how it plays a part in each triangle.