Steps of construction:
ATQ,
1. Let us Draw two lines AB and CD crossing at an angle of ${{75}^{\circ }}$
2. Then draw an angle bisector of $\angle BPD$ with the help of compass
3. Now, draw perpendicular from X on angle bisector with the help of compass ,meeting at O.
4. From point Y, $PX=PY$, draw a perpendicular on angle bisector with the help of compass, meeting at O.
5. So, O is the point which Equal distance from P, X and both the roads.
We know, $\cos \theta =$hypotenuse/base
$cos(37.5)=PO/800$
$0.980243=PO/800$
$PO=0.980243×800$
$PO=784.19m$
Hence $PO=784.19 m$