Question

Use similar triangles to find the distance across the river.

Right triangles and trigonometry
ANSWERED
asked 2021-02-09

Use similar triangles to find the distance across the river.

 

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Expert Answers (2)

2021-02-10

\(\displaystyle∠{A}≅∠{D}\) since all right triangles are congruent and \(\displaystyle∠{B}{C}{A}≅∠{E}{C}{D}\) because vertical angle pairs are congruent. So, \(\displaystyle△{A}{B}{C}∼△{D}{E}{C}\) 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:
\(\displaystyle{B}\frac{{C}}{{E}}{C}={A}\frac{{C}}{{D}}{C}\)
\(\frac{x}{EC}=\frac{48}{0.4}\)
To find EC, use Pythagorean Theorem on \(\displaystyle△{D}{E}{C}\):
\(\displaystyle{D}{E}^{{2}}+{D}{C}^{{2}}={E}{C}^{{2}}\)
\(\displaystyle{0.3}^{{2}}+{0.4}^{{2}}={E}{C}^{{2}}\)
\(\displaystyle{0.25}={E}{C}^{{2}}\)
0.5=EC
Hence,
\(\displaystyle\frac{{x}}{{0.5}}=\frac{{48}}{{0.4}}\)
\(\displaystyle\frac{{x}}{{0.5}}{\left({0.5}\right)}=\frac{{48}}{{0.4}}{\left({0.5}\right)}\)
x=60 mi

34
 
Best answer
2021-08-11

Answer is given below

31

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