The following diagram shows a corner of a field bounded by two walls defined by lines L₁ and L₂. The walls meet at a point A, making an angle of 40°. Farmer Nate has 7 m of fencing to make a triangular enclosure for his sheep. One end of the fence is positioned at a point B on L₂, 10 m from The other end of the fence will be positioned at some point C on L₁, as shown on the diagram. He wants the enclosure to take up as little of the current field as possible.

The following diagram shows a corner of a field bounded by two walls defined by lines L₁ and L₂. The walls meet at a point A, making an angle of 40°. Farmer Nate has 7 m of fencing to make a triangular enclosure for his sheep. One end of the fence is positioned at a point B on L₂, 10 m from The other end of the fence will be positioned at some point C on L₁, as shown on the diagram. He wants the enclosure to take up as little of the current field as possible.

Find the minimum possible area of the triangular enclosure ABC.