Pages

Welcome to William's Math Analysis Blog

Saturday, February 22, 2014

I/D# 1: Unit N Concept 7: Special Right Triangles and the Unit Circle

INQUIRY ACTIVITY SUMMARY
As we know there are several right triangles. However, there are three examples of right triangles that we call "Special Right Triangles." These triangles are the 30, 45, and 60 degrees triangles, which have some special features as shown in the pictures below.
http://dj1hlxw0wr920.cloudfront.net/userfiles/wyzfiles/6d31e6a7-f698-4f44-b2d2-953443b2e5bd.png *(edited by me)

30 degrees
First we labeled the rules of this special right triangle. Them being the hypotenuse is 2x, vertical value = x and horizontal value = x√3.
The next step to this triangle was to find a way to which we can make the hypotenuse equal 1. The way to do this is to divide 2x by itself making it equal 1. As we know, whenever a change is done to a side, the same change must be done to the other sides. Due to this, we divide x and y by 2x leaving us with horizontal value = √3 / 2 and vertical value = 1 / 2
Now you just equal the hypotenuse to r, horizontal value to x and vertical value to y. r = 1, x = √3 / 2, and y = 1 / 2.
Then you draw a plane on the triangle so that the triangle lies on quadrant I
Finally you label the three points on the triangle. The points for this triangle should be (0,0), (√3 / 2, 0), (√3 / 2, 1 / 2)

45 Degrees
First we labeled the rules of this special right triangle. Them being the hypotenuse is x√2, vertical value being x and horizontal value also being x.
The next step to this triangle is to find a way to which we can make the hypotenuse equal 1. The way to do this is to divide x√2 by itself making it equal 1. As we know, whenever a change is done to a side, the same change must be done to the other sides. Due to this, we divide the horizontal and vertical values by x√2 leaving us with horizontal value = √2 / 2 and vertical value = √2 / 2.
Now you just equal the hypotenuse to r, horizontal value to x and vertical value to y. r = 1, x = √2 / 2, and y = √2 / 2.
Then you draw a plane on the triangle so that the triangle lies on quadrant I
In the end, you label the three points on the triangle. The points for this triangle should be (0,0), (√2 / 2, 0), (√2 / 2, √2 / 2)

60 Degree
First we labeled the rules of this special right triangle. Them being the hypotenuse is 2x, vertical value = x√3 and horizontal value = x.
The next step to this triangle was to find a way to which we can make the hypotenuse equal 1. The way to do this is to divide 2x by itself making it equal 1. As we know, whenever a change is done to a side, the same change must be done to the other sides. Due to this, we divide x and y by 2x leaving us with horizontal value = 1 / 2 and vertical value = √3 / 2.
Now you just equal the hypotenuse to r, horizontal value to x and vertical value to y. r = 1, x = 1 / 2, and y =√3 / 2.
Then you draw a plane on the triangle so that the triangle lies on quadrant I.
Finally you label the three points on the triangle. The points for this triangle should be (0,0), (1 / 2, 0), (1 / 2, √3 / 2)