Question

order the sides from least to greatest on 13 and from greatest to least on 14. 13. 14.

Explanation:

Step1: Find the third angle of each triangle

• For triangle \(ABC\):
• Using the angle - sum property of a triangle (\(A + B + C=180^{\circ}\)), if \(A = 92^{\circ}\), \(B = 51^{\circ}\), then \(C=180-(92 + 51)=37^{\circ}\).
• For triangle \(LMN\):
• If \(M = 78^{\circ}\), \(N = 48^{\circ}\), then \(L=180-(78 + 48)=54^{\circ}\).

Step2: Apply the side - angle relationship in a triangle

• In a triangle, the larger the angle, the longer the side opposite it.
• In \(\triangle ABC\):
• Since \(C(37^{\circ})<B(51^{\circ})<A(92^{\circ})\), the sides opposite these angles (using the notation \(a\) opposite \(A\), \(b\) opposite \(B\), \(c\) opposite \(C\)) follow the order \(AB < AC
• In \(\triangle LMN\):
• Since \(N(48^{\circ})<L(54^{\circ})<M(78^{\circ})\), the sides opposite these angles (using the notation \(l\) opposite \(L\), \(m\) opposite \(M\), \(n\) opposite \(N\)) follow the order \(LM> LN>MN\).

Answer:

1. \(AB < AC
2. \(LM> LN>MN\)