I/D2: Unit O - Derive the SRTs

Inquiry Activity Summary 



 1. To start off, we are given an equilateral triangle with a side length of 1 and are asked to derive a 30-60-90 triangle from it. Following the image above, we first cut a straight line down from the center of the equilateral triangle. Since equilateral triangles are 60* on each corner, the line cut results in a 30* at the very top, 90* at the bottom of the cut line, and a 60* at either the left or right corner since it is left untouched to form a 30* special right triangle. . The height is derived from using the Pythagorean formula (a^2+b^2=c^2) and the image above shows how it is done. Since our answer from the Pythagorean results in fractions, we want to make the answer easier to remember so we multiply by 2 to each side length to result in √3 for 60*, n for 30*, and 2n for the 90*. Since the original side lengths are 1, we can infer that we only have to substitute different values and we should result in the same ratio as the original side lengths of 1 triangle. This is where we substitute in a variable like (n) to represent a value that can be used. 

  2. Next, we are given a square with the side lengths and asked for a 45-45-90 triangle. To do this, we simply cut the square in half with a diagonal line. We do this because each corner of the square is 90* and if we were to cut a side in half, it would result in a 45* so that is where we get our special right triangle. To get our hypotenuse, we simply use the Pythagorean formula like above and after plugging everything we can, our C (hypotenuse) ends up as with the ratio as 1 for the 45* and √2 for our 90*. Since the side lengths are 1, we can infer that using different side lengths will still result in the same ratio so we just add an (n) to substitute as our new value so our ratio becomes n,n,n√2.

Inquiry Activity Reflection 

1. "Something I never noticed before about special right triangles is.." there is actually a ratio that we can use to solve for the sides rather than just memorizing something like a unit circle and its value. 

2.  being "Being able to derive these patterns myself aids in my learning because.."able to understand these concepts is much better for me and my test grade than just barely getting the gist of it.