Question

question in \\( \triangle t u v \\), \\( m \angle t = 14 ^ { \circ } \\) and \\( m \angle u = 126 ^ { \circ } \\). which list has the sides of \\( \triangle t u v \\) in order from longest to shortest? answer \\( \bigcirc u v , v t , t u \\) \\( \bigcirc v t , u v , t u \\) \\( \bigcirc u v , v t , t u \\) \\( \bigcirc t u , v t , u v \\) \\( \bigcirc t u , u v , v t \\) \\( \bigcirc v t , t u , u v \\)

Explanation:

Step1: Find the measure of the third angle

The sum of angles in a triangle is \(180^{\circ}\). Let \(\angle V = x\). Then \(x+14^{\circ}+126^{\circ}=180^{\circ}\). So \(x = 180^{\circ}-(14^{\circ}+126^{\circ})=40^{\circ}\).

Step2: Recall the side - angle relationship

In a triangle, the larger the angle, the longer the side opposite it.
Since \(\angle U = 126^{\circ}\), \(\angle V=40^{\circ}\), \(\angle T = 14^{\circ}\), the sides opposite these angles are \(VT\), \(TU\), \(UV\) respectively.
So the order from longest to shortest is \(VT\) (opposite \(\angle U\)), \(TU\) (opposite \(\angle V\)), \(UV\) (opposite \(\angle T\))

Answer:

VT, TU, UV