Answer:
Therefore the Distance across the Pond is
[tex]x=391\ ft[/tex]
Step-by-step explanation:
Given:
Triangle are Similar
AB = 90 ft
AC = 170 ft
BD = 207 ft
DE = x
To Find:
x = ?
Solution:
In Δ ABC and Δ DBE
∠A ≅ ∠D …………..{ measure of each angle is 90° given }
∠ABC ≅ ∠DBE ……….....{Vertical Angle Theorem}
Δ ABC ~ Δ DBE ….{Angle-Angle Similarity test}
If two triangles are similar then their sides are in proportion.
[tex]\dfrac{AB}{DB} =\dfrac{AC}{DE} \textrm{corresponding sides of similar triangles are in proportion}\\[/tex]
Substituting the values we get
[tex]\dfrac{90}{207} =\dfrac{170}{x}\\\\x=23\times 17=391\ ft[/tex]
Therefore the Distance across the Pond is
[tex]x=391\ ft[/tex]
