To determine the order of the sides of triangle XYZ from shortest to longest, we first need to find the measure of angle Z using the fact that the sum of the angles in a triangle is always 180°.
We have:
- \( m∠X = 27° \)
- \( m∠Y = 48° \)
Now, we calculate \( m∠Z \): \[ m∠Z = 180° - m∠X - m∠Y \] \[ m∠Z = 180° - 27° - 48° = 180° - 75° = 105° \]
Now we know:
- \( m∠X = 27° \)
- \( m∠Y = 48° \)
- \( m∠Z = 105° \)
In any triangle, the side opposite the largest angle is the longest, and the side opposite the smallest angle is the shortest.
- Angle X (27°) is the smallest, so the side opposite it, which is \( YZ \), is the shortest.
- Angle Y (48°) is the next largest, so the side opposite it, which is \( XZ \), is the next largest.
- Angle Z (105°) is the largest, so the side opposite it, which is \( XY \), is the longest.
Thus, the order of the sides from shortest to longest is:
- \( YZ \) (shortest)
- \( XZ \) (middle)
- \( XY \) (longest)
Therefore, the correct answer is:
A. \( YZ \), \( XZ \), \( XY \).