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. ∠ A ≅ ∠ D ∠ B ≅ ∠ C ∠ E ≅ ∠ E

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. △ ABE ~ △ DCE Now, notice that AE corresponds to DE and BE corresponds to 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. AE/DE=BE/CE ⇔ 25/8=BE/12 Let's solve this proportion using cross products.

25/8=BE/12

CrossMult

Cross multiply

25 * 12 = 8 * BE

▼

Solve for BE

Multiply

Multiply

300 = 8 * BE

DivEqn

.LHS /8.=.RHS /8.

300/8 = 8 * BE/8

CalcQuot

Calculate quotient

37.5 = 8 * BE/8

MovePartNumRight

a* b/c=a/c* b

37.5 = 8/8 * BE

QuotOne

a/a=1

37.5 = 1 * BE

IdPropMult

Identity Property of Multiplication

37.5 = BE

RearrangeEqn

Rearrange equation

BE = 37.5

The distance from the log ride to the pirate ship is 37.5 meters.