Final answer:
To determine the fourth side of a fenced area, a farmer can use geometric principles, such as the Law of Cosines, or recognize that opposite sides of a rectangle are equal. The practice of using a single crop over a large area is known as monoculture. Witnessing the difference in land quality between fenced and non-fenced areas in Africa points to the importance of sustainable farming practices.
Step-by-step explanation:
When a farmer wants to fence off a four-sided plot of land and has already measured three sides, the fourth side's length and orientation can be determined using principles of geometry. For a rectangular field, the opposite sides are equal; therefore, if sides A, B, and C are known, side D must be equal to side B (assuming A and C are the initial pair of opposite sides). However, if the shape is irregular, then the Law of Cosines or another geometric method may be needed to find the length and direction of the fourth side.
The practice of planting a single crop over a large area, like the 100 hectares of soybeans mentioned, is known as monoculture. This can lead to issues such as soil depletion and increased vulnerability to pests, contrasting with practices like crop rotation that can preserve the land's fertility over time.
In the case of Africa and the use of fenced land versus nomadic usage, the difference in sustainability practices is stark. The fenced land, owned by farmers who rotated grazing animals and periodically allowed fields to rest, remained fertile, while the land used by nomads without such planning suffered severe degradation.
Similarly, the new landowner calculating the third side of her triangular piece of flat land would apply the Law of Cosines, or she could graphically add the displacement vectors such that the third side, or vector C, would close the triangle by connecting the end of vector B back to the starting point of vector A.