A point x is 34m due to east of a point Y . The bearing of a flagpole from x and Y are N18°W And N40°E respectively .

The distance from point Y to the flag post measures 38.13 m. Step-by-step explanation: Assuming point Y is located at the intersection of both lines shown. Point X is positioned 34 meters east of point Y. The flagpole at point X is observed at a bearing of N18°W, meaning it creates an angle of 18° to the west from the north at point X. Conversely, at point Y, the flagpole has a bearing of N40°E, which makes a 40° angle towards the east from the north. Considering ∆ AXY as a right triangle, the angle FXY is established. Then, concerning ∆ BYX as another right triangle, the angle FYX is also determined. To find the third angle ∠YFX in triangle FYX, the angle sum property of triangles can be applied: ∠YFX + ∠FYX + ∠FXY = 180° Thus, we have: ∠YFX + 50° + 72° = 180° leading to ∠YFX = 58°. Now we can calculate the distance FY using the sine rule.