Use similar triangles to find the distance across the river.

Use similar triangles to find the distance across the river.

Question
Use similar triangles to find the distance across the river.

Answers (1)

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:
\(\displaystyle{B}\frac{{C}}{{E}}{C}={A}\frac{{C}}{{D}}{C}\)
PSKx/EC=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
0

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