Answer:
will show you two (2) ways to solve this problem.
A diagram is needed to see what is going on....
  
Without loss of generality (WLOG)
The wall is on the right. The ladder leans against the wall
with a POSITIVE slope, from SW to NE (quadrant 3 to quadrant 1).
The measure from the bottom of the ladder to the wall is 6.
  
  
Option 1:
  
 The ladder, ground and wall form a right triangle.
  
 The hypotenuse (ladder) is 14 feet.
  
  The bottom of the ladder is 6 feet from the wall,
   so the base of this right triangle is 6 feet.
  
 The top of the ladder to the ground represents
the missing leg of the right triangle.
  
The pythagorean theorem applies, which says
  6^2 + h^2 = 14^2   where h is the height
                                  of the top of the ladder to the ground
  
36 + h^2 = 196
  
  h^2 = 196 - 36
  
 h^2  = 160
  
 h = sqrt(160)
  
    = sqrt(16 * 10)
  
     = sqrt(16)* sqrt(10)
  
     = 4*sqrt(10) <--- exact answer
  
     = 4 * 3.16227766016838....
  
      = 12.64911....
  
     12.65 <--- rounded to 2 digits as directed
  
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Option #2: using trig
  
With respect to the angle formed by the bottom of the
ladder with the ground
   cos T = 6/14 = 3/7  
  T = inverse-cosine(3/7) = 64.623006647 degrees
  
  sin(64.623006647) = h/14
  
  h = 14*sin(64.62300647) = 12.6491106 <--- same answer                        
hope this helps
Step-by-step explanation: