My maths isn't the strongest, and I would like to know how to calculate whether one object is facing another within some given angle.
At the moment I calculate whether objects are behind or in front of each other just by using a dot product of the facing direction of one object and the vector between that object and another, if it is positive the object is facing the other object. This isn't accurate enough for my purpose however, and I would like to be able to tell whether an object is within a given number of degrees/radians of another object's facing direction.
Your method is good, you just have to normalize your vectors (divide them by their lengths). If you do that, their dot product will be equal to cos( angle between them ).