The relation {(4,10), (1,9), (5,10), (1,10)} is a function

it is not a function

for functions to work, there can only be one y value per x value aka if you see a set like this:  

{(4,2), (6,5), (10,1), (3,6), (6,7)}  

It is not a function because there are two y values (5 and 7) for one x value (6).

Angle A =19°, c=36 ft, a=20ft
To find all the sides & angles of this triangle let's  apply the Law of sine:

sinA/a =sinC/c ==> sin19°/20 = sinC/36 =0.325568/20 = sinC/36

sinC =0.5860 & arcsin(0.5860) ==> ANGLE C=35.8°

You can follow the same methodology to find the unknown sides and/or angle