Question

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

What is the distance across the pond?

Answer 1

The calculated distance across the pond is 391 feet

How to determine the distance across the pond?

From the question, we have the following parameters that can be used in our computation:

The figure

Also, we have that

The figures are similar triangles

Using the proportional equation of similar triangles, we have

x/207 = 170/90

This gives

x = 207 * 170/90

Evaluate

x = 391

Hence, the distance across the pond is 391 feet

Answer 2

Therefore the Distance across the Pond is

`x=391\ ft`

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.

`(AB)/(DB) =(AC)/(DE) \textrm{corresponding sides of similar triangles are in proportion}\\`

Substituting the values we get

`(90)/(207) =(170)/(x)\\\\x=23* 17=391\ ft`

Therefore the Distance across the Pond is

`x=391\ ft`