Exercise 16 Page 559

We are given following diagram and want to find the depth of the water $d.$ Let's first show that triangles $VWX$ and $VYZ$ are similar. Once we know that the triangles are similar, we can use their proportional relationship to find the missing distance.

From the angle markers shown in the diagram, we can see that $\angle X$ is congruent to $\angle Z$ and $\angle W$ is congruent to $\angle Y.$ Since two angles of $△VWX$ are congruent to two angles of $△VYZ,$ they are similar by the Angle-Angle (AA) Similarity rule. Now, notice that $\overline{VW}$ corresponds to $\overline{VY}$ and that $\overline{WX}$ corresponds to $\overline{YZ}.$ Corresponding sides of similar figures will have proportional lengths. We know that $\overline{VW}=3$ meters, $\overline{VY}=62$ meters, and $\overline{WX}=5$ meters, so we will use these lengths to write a proportion. Let's solve this proportion using cross products. The water is about $103.3$ meters deep.