Question

triangle inequality theorem checkpoin

1. find m∠a then list the sides from shortest to longest.

m∠a =

shortest: middle: longest:

Explanation:

Step1: Find \(m\angle A\)

The sum of angles in a triangle is \(180^{\circ}\).

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Step2: Relate angles and sides

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

• Angle \(C = 35^{\circ}\), side opposite \(C\) is \(AB\).
• Angle \(A=75^{\circ}\), side opposite \(A\) is \(BC\).
• Angle \(B = 70^{\circ}\), side opposite \(B\) is \(AC\).

Since \(35^{\circ}<70^{\circ}<75^{\circ}\), then \(AB < AC

Answer:

\(m\angle A = 75^{\circ}\); Shortest: \(AB\), Middle: \(AC\), Longest: \(BC\)