Question

station 9: arrange the angles from greatest to least.

Explanation:

Step1: Recall Triangle Angle-Side Relationship

In a triangle, the larger the side length, the larger the angle opposite to it. This is based on the Law of Sines (or the basic angle - side relationship in triangles: if \(a,b,c\) are the side lengths opposite angles \(A,B,C\) respectively, then \(a > b>c\) implies \(A > B > C\)).

Step2: Identify Sides and Opposite Angles

• Side \(BC = 27\) is opposite angle \(A\).
• Side \(AC=15\) is opposite angle \(B\).
• Side \(AB = 21\) is opposite angle \(C\).

Step3: Compare Side Lengths

Compare the lengths of the sides: \(27>21 > 15\).

Step4: Determine Angle Order

Since the side opposite angle \(A\) (\(BC = 27\)) is the longest, angle \(A\) is the largest. The side opposite angle \(C\) (\(AB=21\)) is longer than the side opposite angle \(B\) (\(AC = 15\)), so angle \(C\) is larger than angle \(B\). So the order of angles from greatest to least is \(\angle A>\angle C>\angle B\).

Answer:

\(\angle A>\angle C>\angle B\)