1. The problem involves finding the distance between points X and Y given their bearings and distances from point O. 2. Point X is located 40 m from O at a bearing of 047° clockwise from north. 3. Point Y is located 75 m from O at a bearing of 317° clockwise from north. 4. The angle between the two bearings is $$317^\circ - 47^\circ = 270^\circ$$, but since bearings wrap around, the smaller angle between the two lines is $$360^\circ - 270^\circ = 90^\circ$$. 5. We can model triangle OXY with sides OX = 40 m, OY = 75 m, and angle $$\angle XOY = 90^\circ$$. 6. Using the Law of Cosines or recognizing this is a right triangle, the distance XY is: $$XY = \sqrt{OX^2 + OY^2 - 2 \times OX \times OY \times \cos(90^\circ)} = \sqrt{40^2 + 75^2} = \sqrt{1600 + 5625} = \sqrt{7225} = 85\text{ m}$$ 7. Therefore, the distance between points X and Y is 85 meters.