Always sketch the triangle with the letters
A,B,C,a,b,c, or whatever letters are to be
used, and put in the given parts:

  

The three major trig functions are

sin(A) =  = 

cos(A) =  = 

tan(A) =  = 

We are given "a", the opposite side.  So we will
use only the two trig functions that contain "a",
the opposite side.  So we will use only the sine 
and the tangent.  We will not use the cosine, 
because it does not contain the given side "a", 
the opposite.

sin(A) = = 
sin(60°13') = 

Multiply both sides by c

c·sin(60°13') = 6.5143

Divide both sides by sin(60°13')

c = 

If you have a TI-84 calculator, calculate that by

6.5143÷sin(60+13/60) ENTER

Get c = 7.50573233.  Round the same way the given side is
rounded, 4 decimal places, so

c = 7.5057 

[If you get -12.965603553, which is wrong, it's
because you have your calculator in radian mode,
so press MODE, press the down arrow key twice
to go down to RADIAN, and the right arrow key 
once, and press ENTER to highlight. Then press
2ND MODE, and do it again.]

tan(A) = = 
tan(60°13') = 

Multiply both sides by b

b·tan(60°13') = 6.5143

Divide both sides by tan(60°13')

b = 

If you have a TI-84 calculator, calculate that by

6.5143÷tan(60+13/60) ENTER

Get b = 3.728258751.  Round the same way the given side is
rounded, 4 decimal places, so

b = 3.7283.

You just have to find angle B.  A and B must have sum 90°,
so

A + B = 90°
    B = 90° - 60°13'

To do that write 90° as 89°60'

Then subtract:

 89°60'
-60°13'
-------
 29°47'

So:

 B=29°47'
 b=3.7283
 c=7.5057

Edwin