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Posted 2 months ago

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 55,6555^{\circ}, 65^{\circ}, and 7575^{\circ}.
\hline Angle & 5555^{\circ} & 6565^{\circ} & 7575^{\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 opposite leg length  adjacent leg length \frac{\text { opposite leg length }}{\text { adjacent leg length }} & 1.43 & 2.14 & 3.73 \\

Use the table to approximate mDm \angle D in the triangle below.

Choose 1 answer:
(A) 5555^{\circ}
(B) 6565^{\circ}
(C) 7575^{\circ}
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Answer from Sia
Posted 2 months ago
Solution by Steps
step 2
The ratio is calculated as 6.1/6.70.916.1/6.7 \approx 0.91 based on the asksia-ll calculation list
step 3
Compare the calculated ratio to the ratios given in the table for 5555^{\circ}, 6565^{\circ}, and 7575^{\circ}
step 4
The ratio closest to 0.910.91 in the table is for the angle 6565^{\circ}, which has a ratio of 0.910.91
step 5
Therefore, the measure of angle D is approximately 6565^{\circ}
[question number] Answer
Key Concept
Using ratios to determine angle measures in right triangles
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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