I/D#2: Unit O Concept 7-8: Deriving the pattern of SRT

Inquiry Activity Summary:

45,45,90 degrees SRT
To begin, we need to label each side equals to 1. Next, the equallateral needs to be cut in half in order to find the 45,45,90 degrees triangle. 

Since the given information is only 2 sides of the triangles, we need to find the missing sides. You can find the missing side by using the pythagorean theorem of a^2+b^2=c^2. The legs of the triangle will always A and B while the hypothenus is C. When it is plugged in, it should be (1)^2+(1)^2=C^2. After solving, you should get C= radical 2.

For it to be a SRT, N should be added to the pattern because the value can be change anytime. The final pattern of the 45,45,90 should be 1n,1n, and N radical 2. 

30,60,90 SRT

Now we are going to look at another special right triangle. It is the 30,60,90 degrees. To begin, we label each side equalss to 1. Then we cut the triangle in half.

Next, the 1 on the short leg becomes 1/2 because the triangle has been cut half. The hypotenus will stay as a value of 1. The pythagorean theoream needs to be use in order to find the other missing side of the triangle

The pythagorean theorem is a^2+b^2=c^2 After solving, you should get C=radical 3/2

Since the value of each side does not follow the pattern, we must find the pattern by multiplying everything by 2. 

Finally, we should get the pattern of 1,2,and radical 3. However, the n needs to be there because the value of these can be change depending on the triangle.

Inquiry Activity Reflection:

The coolest thing I learned from this activity was that we can pattern came from a triangle that has all side equals to 1.

The coolest thing I learned from this activity was I can derive the formula if I were to forget it during the test or in the future.