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 ∠X is congruent to ∠Z and ∠W is congruent to ∠Y.
∠X ≅ ∠Z
∠W ≅ ∠YSince two angles of △ VWX are congruent to two angles of △ VYZ, they are similar by the Angle-Angle (AA) Similarity rule.
â–³ VWZ ~ â–³ VYZ
Now, notice that VW corresponds to VY and that WX corresponds to YZ.
Corresponding sides of similar figures will have proportional lengths. We know that VW=3 meters, VY=62 meters, and WX=5 meters, so we will use these lengths to write a proportion.
VW/VY=WX/YZ ⇔ 3/62=5/d
Let's solve this proportion using cross products.
