16) C 

This is a tricky question.

First, draw a line perpendicular to AB from C. Label the line be CP.

We have tan A =  CP  =  1 
                           AP      6

So, CP = 1, AP = 6

We have tan B =  CP  =   2  
                             BP       3

Since CP = 1, BP = (3 ÷ 2) = 1.5

Since BP = 1.5, then AP = 6

AB = (AP + BP) = (1.5 + 6) = 7.5

Since M is the mid point, BM = (7.5 ÷ 2) = 3.75

PM = (BM – BP) = (3.75 – 1.5) = 2.25

tanθ =  CP 
            PM

  CP   =    1    
 PM       2.25

   1     =     4   
2. 25         9