Question

list the sides in order from shortest to longest
triangle image with angles at a: 63°, b: 70°, c: 47°
options:

• bc, ab, ac
• ab, bc, ac
• ac, bc, ab
• bc, ac, ab

Explanation:

Step1: Recall Triangle Side-Angle Relationship

In a triangle, the longer side is opposite the larger angle, and the shorter side is opposite the smaller angle.

Step2: Identify Angles and Opposite Sides

• Angle at \( A \): \( 63^\circ \), opposite side \( BC \)
• Angle at \( B \): \( 70^\circ \), opposite side \( AC \)
• Angle at \( C \): \( 47^\circ \), opposite side \( AB \)

Step3: Order Angles from Smallest to Largest

Angles: \( 47^\circ \) (at \( C \)) \( < 63^\circ \) (at \( A \)) \( < 70^\circ \) (at \( B \))

Step4: Order Sides (Opposite Angles)

Since side opposite smaller angle is shorter:

• Opposite \( 47^\circ \) (smallest angle): \( AB \) (shortest side)
• Opposite \( 63^\circ \): \( BC \)
• Opposite \( 70^\circ \) (largest angle): \( AC \) (longest side)

So order from shortest to longest: \( AB, BC, AC \)

Answer:

AB, BC, AC (corresponding to the blue option: AB, BC, AC)