Question

relating the side lengths and angle measures of one triangle
given triangle ghj, the measure of angle g equals 110, the measure of
angle j equals 40, and the measure of angle h equals 30. complete the
following statements.
since angle g angle, the opposite side, jh, is
the largest
the smallest
the order of the longest to shortest is

Explanation:

Step1: Recall triangle side - angle relationship

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

Step2: Compare angle measures

Given \(m\angle G = 110^{\circ}\), \(m\angle J=40^{\circ}\), \(m\angle H = 30^{\circ}\). Since \(110^{\circ}>40^{\circ}>30^{\circ}\) (i.e., \(\angle G>\angle J>\angle H\)).

Step3: Determine side lengths

The side opposite \(\angle G\) is \(JH\), the side opposite \(\angle J\) is \(GH\), and the side opposite \(\angle H\) is \(GJ\).

Answer:

Since angle \(G\) is the largest angle, the opposite side \(JH\) is the longest. The order of the side lengths from longest to shortest is \(JH>GH>GJ\)