Exercise 5 Page 557

We are given a diagram and we want to find the distance from the log ride to the pirate ship. Let's first label and show that triangles 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 all the corresponding angles are congruent. Since at least two of the three angles of $△ABE$ are congruent to two angles of $△DCE,$ they are similar by the rule for Angle-Angle (AA) Similarity. Now, notice that $\overline{AE}$ corresponds to $\overline{DE}$ and $\overline{BE}$ corresponds to $\overline{CE}.$ Remember that corresponding sides of similar figures will have proportional lengths. We know that $AE=25$ meters, $DE=8$ meters, and $CE=12$ meters. We can use these lengths to write a proportion. Let's solve this proportion using cross products. The distance from the log ride to the pirate ship is $37.5$ meters.