Question

select the correct answer from each drop-down menu.
in triangle abc, m∠a = 36°, m∠b = 84°, and m∠c = 60°.
the side lengths, in order from greatest to least, are
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Explanation:

Step1: Recall angle - side relationship

In a triangle, the larger the angle, the longer the side opposite to it. This is based on the principle that in a triangle, the side opposite a larger angle is longer.

Step2: Order the angles

Given \(m\angle A = 36^{\circ}\), \(m\angle B=84^{\circ}\), \(m\angle C = 60^{\circ}\). We order the angles from largest to smallest: \(\angle B>\angle C>\angle A\) (since \(84^{\circ}>60^{\circ}>36^{\circ}\)).

Step3: Determine the opposite sides

The side opposite \(\angle A\) is \(BC\), the side opposite \(\angle B\) is \(AC\), and the side opposite \(\angle C\) is \(AB\).
Since \(\angle B>\angle C>\angle A\), the sides opposite them (in order) will be \(AC > AB>BC\).

Answer:

\(AC\), \(AB\), \(BC\)