Question

Surveyors need to measure the distance across a pond. they created similar triangles in this picture.

Answer 1

Answer:

Therefore the Distance across the Pond is

$x=391\ ft$

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.  

$\dfrac{AB}{DB} =\dfrac{AC}{DE} \textrm{corresponding sides of similar triangles are in proportion}$  

Substituting the values we get

$\dfrac{90}{207} =\dfrac{170}{x}\\\\x=23\times 17=391\ ft$

Therefore the Distance across the Pond is

$x=391\ ft$