Solve for the missing length and the other two angles in the triangle below.

To find AC, use the Law of Cosines:  AC² =  5² + 8² - 2·5·8·cos(20^o)

 

Then, you can find the size of angle(C) --

 

To find angle(C), use the Law of Sines:  sin(C) / 5  =  sin(20^o) / AC               

 

Then, you can find the size of angle(A) by subtracting angles B and C from 180^o.

 

[Warning!  Don't use the Law of Sines to find the largest angle in a triangle -- the answer that your calculator gives you may not be the correct answer!]