The bearing of a house from point A is 319 from a point B, 317m due east of A, the bearing of the house is 288. How far is the house from A?

Not enough information is 319 and 288 in meters? Maybe it's the difference between the two? 319-288= 27?
Then you tell us that B is 317m due east from A. Sounds like a geometry problem, try drawing it out with using a scale(ex 1cm=10m) and grid paper.

The answer sounds like 317meters, it might be a test of how well you understood the question, i.e. how far are the two houses if you say it's 317meters east from the house. But if 319 and 288 are height measurement then you might need to draw a triangle and take into account the difference in alttitude from one to the other too.
Good luck