Special Right Triangles

In today's class we started off by correcting the previous homework assigned for Carnival week.
After we finished correcting we studied Special Right Triangles, and with it Theorems 8-6 and 8-7.

Theorem 8-6:

If: Right Triangle with angles measuring 45-45-90
Then: Hypothenuse of that triangle is (square root of 2) times the leg

Another important thing about this Theorem is that if you want to find the leg instead of the Hypothenuse then you can use the following equation: The leg equals the Hypothenuse divided by (square root of 2)

Theorem 8-7:

If: Right Triangle with angles measuring 30-60-90

Then: Hypothenuse is twice the shorter leg

Following the same idea from the previous Theorem if you are looking for the longer leg instead of the shorter one then you can use: Longer leg equals (square root of 3) times the shorter leg.

To find, in this case, the longer leg instead of the shorter one is just like appling COS,TAN,SIN^-1 to find x in an equation: When you want to find a measure that is not the one presented specifically in the Theorem.

After these Theorems Ms. Saatkamp taught us a very usefull table to memorize about Sin, Cos and Tan's:

As we can see, all the values in SIN and COS are square roots of 1,2,3 and 3,2,1 and all of them being over two, while the values in TAN is the corresponding value of SIN/COS

To finish class the homework was assigned: Page 409 #11-27all

PS.: Ms. Saatkamp, there were many problems to upload images here and the Internet was very slow, when I tried to upload an image it said "Houve erros durante o carregamento" every single time. Then i just passed my table to word and sent it to your email for you to see I've done it, but still couldn't upload it into this post, thank you.