$18 \cdot 52$ A rectangular field has a power pole standing in it. If the distances from the bottom of the pole to three vertices are known, then the distance from the bottom of the pole to the fourth vertex
(A) can be determined.
(B) can only be determined if the lengths of two sides of the field are known.
(C) can be determined if and only if the length of one side of the field is known.
(D) can be determined if and only if the field is a square.
[Solution] Let the rectangle be $A B C D$ (as shown in the figure), and draw $E F \perp A B$ through $P$.
Let $A E=x, B E=y, P D=d$.
Also, $A P=a, \quad B P=b, \quad C P=c$.
By the Pythagorean theorem, we have
$$
\left\{\begin{array}{l}
b^{2}-a^{2}=y^{2}-x^{2} \\
c^{2}-d^{2}=y^{2}-x^{2}
\end{array}\right.
$$

Therefore, $b^{2}-a^{2}=c^{2}-d^{2}$,
which means $d^{2}=a^{2}+c^{2}-b^{2}$, or $d=\sqrt{a^{2}+c^{2}-b^{2}}$.
Hence, the answer is $(A)$.