Question

Math

Posted 2 months ago

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Given the measure of an acute angle in a right triangle, we can tell the ratios of the lengths of the triangle's sides relative to that acute angle.
Here are the approximate ratios for angle measures $55^{\circ}, 65^{\circ}$, and $75^{\circ}$.
\begin{tabular}{|c|c|c|c|}
\hline Angle & $55^{\circ}$ & $65^{\circ}$ & $75^{\circ}$ \\
\hline \begin{tabular}{l}
adjacent leg length \\
hypotenuse length
\end{tabular} & 0.57 & 0.42 & 0.26 \\
\hline \begin{tabular}{l}
opposite leg length \\
hypotenuse length
\end{tabular} & 0.82 & 0.91 & 0.97 \\
\hline$\frac{\text { opposite leg length }}{\text { adjacent leg length }}$ & 1.43 & 2.14 & 3.73 \\
\hline
\end{tabular}
Use the table to approximate $m \angle D$ in the triangle below.
Choose 1 answer:
(A) $55^{\circ}$
(B) $65^{\circ}$
(C) $75^{\circ}$
```

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Answer from Sia

Posted 2 months ago

Solution by Steps

step 2

The ratio is calculated as $6.1/6.7 \approx 0.91$ based on the asksia-ll calculation list

step 3

Compare the calculated ratio to the ratios given in the table for $55^{\circ}$, $65^{\circ}$, and $75^{\circ}$

step 4

The ratio closest to $0.91$ in the table is for the angle $65^{\circ}$, which has a ratio of $0.91$

step 5

Therefore, the measure of angle D is approximately $65^{\circ}$

[question number] Answer

B

Key Concept

Using ratios to determine angle measures in right triangles

Explanation

The ratio of the lengths of sides in a right triangle is related to the measure of its angles. By comparing the calculated ratio of side lengths to known ratios for specific angles, we can approximate the measure of an angle.

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