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$\frac{ ext { opposite leg length }}{ ext { adjacent leg length }}$ & 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) $75^{\circ}$

Question

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$\frac{	ext { opposite leg length }}{	ext { adjacent leg length }}$ & 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) $75^{\circ}$

Accepted Answer

∻Solution by Steps∻ ‖ step 1 ⋮ Calculate the ratio of the opposite leg length to the adjacent leg length using the given side lengths of the right triangle. ‖ ‖ 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.⚹◊What is the ratio of the opposite leg length to the adjacent leg length for the right triangle with sides labeled EF, FD, and DE, with lengths 6.1 and 6.7?⍭ Generate me a similar question◊

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