Let's begin with recalling the $S A S$ inequality.

If \overline{B C} = \overline{G H} and \overline{A C} = \overline{F H}, and ∠ C > ∠ H then \overline{A B} > \overline{F G}

In our exercise we are asked to use this inequality to explain why the given method is effective. Let's draw the simplified picture describing this situation.

Notice that since the stake is tied to the trunk of the tree, the distance between the ground and the place on the trunk of this tree where the stake is tied is constant. Similarly, the distance on the ground between the tree and the end of the stake is constant. Now, let's imagine that the tree tilts to the left.

As we can see, when the tree tilts to the left, the angle between the tree and the ground becomes larger. According to the $S A S$ inequality, this means that $\overline{F E}$ should be greater than $\overline{C B} .$ However, this side corresponds to the stake so it cannot change its length. Now, let's check what would happen if the tree tilts to the right.

This time, when the tree tilts to the right, the angle between it and the ground becomes smaller. By the $S A S$ inequality, we know that $\overline{F E}$ should be less than $\overline{C B} .$ Again, as this side corresponds to the stake, it cannot change its length.

Therefore, with a constant length of the stake, it is impossible for the tree to tilt either to the left or the right side, so the given method is effective.

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