Column A: r
Column B: v
Column A: r
Column B: v
Show Hint
- The quantity in Column A is greater.
- The quantity in Column B is greater.
- The two quantities are equal.
- The relationship cannot be determined from the information given.
The Correct Option is B
Solution and Explanation
The question asks to compare the measures of two angles within a single triangle, given the lengths of all three sides.
Step 2: Key Formula or Approach:
The Triangle Inequality Theorem relates the side lengths of a triangle to its angles. Specifically, the angle opposite a longer side is larger than the angle opposite a shorter side.
Step 3: Detailed Explanation:
The diagram shows a triangle with side lengths 5, 6, and 7.
Column A: The angle \(r\) is opposite the side with length 5.
Column B: The angle \(v\) is opposite the side with length 7.
We compare the lengths of the sides opposite these angles. The side opposite \(v\) is 7, and the side opposite \(r\) is 5.
Since \( 7>5 \), the angle opposite the side of length 7 must be greater than the angle opposite the side of length 5.
Therefore, \( v>r \).
Step 4: Final Answer:
The quantity in Column B (\(v\)) is greater than the quantity in Column A (\(r\)).
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