Use $∆ABC$ at right to complete the following problems. 

1. Calculate the exact length of $\overline {AB}$ in terms of $n$. 

   Steps (a):

   $AB^2 = (n\sqrt{2})^2 + (n\sqrt{2})^2$ 

   $AB^2 = 2n^2+2n^2$ 

2. If $n=2$, what is the value of $\sin(A)$? If $n=12$, what is the value of $\sin(A)$?

   Hint (b):

   $\operatorname {sin}(A) = \frac{\text{opposite}}{\text{hypotenuse}}$ 

3. In terms of $n$, what is the value of $\sin(A)$?

   Answer (c):

   ${\frac{\sqrt{2}}{2}}$ 

4. What does this tell you about $\sin(45°)$? 

   Answer (d):

   It does not matter what the side length is as long as $A=45°$.

5. What about $\cos(45°)$?  

   Hint (e):

   $\cos(45°)=\sin(45°)$