We are given following diagram and we want to find the distance across the river. Let's first show that triangles CBA and DBE are similar. Once we know that the triangles are similar, we can use their proportional relationship to find the missing distance.
From the picture, we can see that ∠ A and ∠ E are right angles. This means that they have the same measures. They are congruent. Also we can see that ∠ CBA and ∠ DBE are vertical angles. We know that vertical angles are congruent. Let's mark it on our graph.
Since two angles of △ CBA are congruent to two angles of △ DBE, they are similar by the rule for Angle-Angle (AA) Similarity.
△ CBA ~ △ DBE
Now, notice that BE corresponds to BA and AC corresponds to ED.
Remember that corresponding sides of similar figures will have proportional lengths. We know that BE= 350 meters, BA= 140 meters, and ED= 300 meters. We can use these lengths to write a proportion.
BA/BE=AC/ED ⇔ 140/350=AC/300
Let's solve this proportion using cross products.
