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Calculate the ratios in the last three columns and round to three decimal places. Enter the results in the table below.

[tex]\[
\begin{tabular}{|c|c|c|c|c|c|c|}
\hline
Triangle & Hypotenuse & Opposite & Adjacent & \(\frac{\text{opp}}{\text{hyp}}\) & \(\frac{\text{adj}}{\text{hyp}}\) & \(\frac{\text{opp}}{\text{adj}}\) \\
\hline
1 & 2.742 & 0.476 & 2.700 & 0.174 & 0.985 & 0.176 \\
\hline
2 & 2.742 & 0.710 & 2.649 & 0.259 & 0.966 & 0.268 \\
\hline
3 & 2.742 & 0.938 & 2.577 & 0.342 & 0.941 & 0.364 \\
\hline
4 & 2.742 & 1.159 & 2.485 & 0.423 & 0.906 & 0.466 \\
\hline
5 & 2.742 & 1.573 & 2.246 & 0.574 & 0.819 & 0.700 \\
\hline
\end{tabular}
\][/tex]



Answer :

GinnyAnswer
Let's complete the table step-by-step by correctly calculating and filling in the required ratios for each of the triangles. We'll ensure that all values are rounded to three decimal places.

The columns to be filled are:
- opp/hyp (opposite divided by hypotenuse)
- adj/hyp (adjacent divided by hypotenuse)
- opp/adj (opposite divided by adjacent)

The correctly filled in table is:
[tex]\[ \begin{array}{|c|c|c|c|c|c|c|} \hline \text{Triangle} & \text{Hypotenuse} & \text{Opposite} & \text{Adjacent} & \text{opp/hyp} & \text{adj/hyp} & \text{opp/adj} \\ \hline 1 & 2.742 & 0.4761433 & 2.7003429 & 0.174 & 0.985 & 0.176 \\ \hline 2 & 2.742 & 0.70968182 & 2.6485686 & 0.259 & 0.966 & 0.268 \\ \hline 3 & 2.742 & 0.93781923 & 2.5766372 & 0.342 & 0.94 & 0.364 \\ \hline 4 & 2.742 & 1.1588193 & 2.485096 & 0.423 & 0.906 & 0.466 \\ \hline 5 & 2.742 & 1.5727466 & 2.2461149 & 0.574 & 0.819 & 0.7 \\ \hline \end{array} \][/tex]

To summarize the ratios filled:
- For Triangle 1:
- [tex]\( \text{opp/hyp} = 0.174 \)[/tex]
- [tex]\( \text{adj/hyp} = 0.985 \)[/tex]
- [tex]\( \text{opp/adj} = 0.176 \)[/tex]

- For Triangle 2:
- [tex]\( \text{opp/hyp} = 0.259 \)[/tex]
- [tex]\( \text{adj/hyp} = 0.966 \)[/tex]
- [tex]\( \text{opp/adj} = 0.268 \)[/tex]

- For Triangle 3:
- [tex]\( \text{opp/hyp} = 0.342 \)[/tex]
- [tex]\( \text{adj/hyp} = 0.94 \)[/tex]
- [tex]\( \text{opp/adj} = 0.364 \)[/tex]

- For Triangle 4:
- [tex]\( \text{opp/hyp} = 0.423 \)[/tex]
- [tex]\( \text{adj/hyp} = 0.906 \)[/tex]
- [tex]\( \text{opp/adj} = 0.466 \)[/tex]

- For Triangle 5:
- [tex]\( \text{opp/hyp} = 0.574 \)[/tex]
- [tex]\( \text{adj/hyp} = 0.819 \)[/tex]
- [tex]\( \text{opp/adj} = 0.7 \)[/tex]

This completes the table with all values correctly rounded to three decimal places.

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