Question

list the side lengths of δstu in order from shortest to longest.
u
61b
s 49b b+69° t
□ < <

Explanation:

Step1: Find the value of \( b \)

In a triangle, the sum of interior angles is \( 180^\circ \). So, \( 49b + 61b + (b + 69) = 180 \). Combine like terms: \( 111b + 69 = 180 \). Subtract 69 from both sides: \( 111b = 111 \). Divide by 111: \( b = 1 \).

Step2: Calculate each angle

• Angle \( S \): \( 49b = 49(1) = 49^\circ \)
• Angle \( U \): \( 61b = 61(1) = 61^\circ \)
• Angle \( T \): \( b + 69 = 1 + 69 = 70^\circ \)

Step3: Relate angles to sides (Larger angle → Longer side)

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

• Side opposite \( S \) ( \( 49^\circ \)): \( TU \)
• Side opposite \( U \) ( \( 61^\circ \)): \( ST \)
• Side opposite \( T \) ( \( 70^\circ \)): \( SU \)

So, order of sides from shortest to longest: \( TU < ST < SU \)

Answer:

\( TU < ST < SU \)