Get the answer to "Use similar triangles to find the distance across..."

High School
Geometry
Trigonometry
Right triangles and trigonometry

illusiia

Answered question

2021-02-09

Use similar triangles to find the distance across the river.

Answer & Explanation

Jaylen Fountain

Skilled2021-02-10Added 169 answers

$∠ A ≅ ∠ D$ since all right triangles are congruent and $∠ B C A ≅ ∠ E C D$ because vertical angle pairs are congruent. So, $△ A B C \sim △ D E C$ by A.
Similar figures have corresponding side lengths that are proportional. If x is the distance across the river (which is BC), then we can write:
$B \frac{C}{E} C = A \frac{C}{D} C$
$\frac{x}{E C} = \frac{48}{0.4}$
To find EC, use Pythagorean Theorem on $△ D E C$ :
$D E^{2} + D C^{2} = E C^{2}$
${0.3}^{2} + {0.4}^{2} = E C^{2}$
$0.25 = E C^{2}$
0.5=EC
Hence,
$\frac{x}{0.5} = \frac{48}{0.4}$
$\frac{x}{0.5} (0.5) = \frac{48}{0.4} (0.5)$
x=60 mi

Jeffrey Jordon

Expert2021-08-11Added 2605 answers

Answer is given below

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