Question

u2 l4 review cards
station 9: arrange the angles from greatest to least.
(there is a triangle labeled with vertices a, b, c. side ac is 15, side ab is 21, side bc is 27)

Explanation:

Step1: Recall Triangle Angle-Side Relationship

In a triangle, the larger the side length, the larger the angle opposite to it. So we first identify the sides and their opposite angles.

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

Step2: Compare Side Lengths

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

Step3: Determine Angles Order

Since the angle opposite the longest side is the largest, and vice versa:

• Angle opposite \( 27 \) (side \( BC \)) is \( \angle A \), so \( \angle A \) is the largest.
• Angle opposite \( 21 \) (side \( AB \)) is \( \angle C \), so \( \angle C \) is the middle.
• Angle opposite \( 15 \) (side \( AC \)) is \( \angle B \), so \( \angle B \) is the smallest.

So the order from greatest to least is \( \angle A > \angle C > \angle B \).

Answer:

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