By alternate angles on parallel lines, we can deduce various other angles in the diagram.
After filling in several angles, we note that , so the paths actually form a right angled triangle .
Then, by Pythagoras' Theorem,
So the distance from his door to the pole is m.
Next, to find the beaing of H from P, note that
Now, note that by alternate angles on parallel lines,
So , approximately.
Therefore the bearing to H from P is , or, if you prefer,