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 is the largest angle, the opposite side, jh, is the longest side
the order of the side lengths from longest to shortest is
gj, gh, and hj
hj, gh, and gj
hj, gj, and gh

Explanation:

Step1: Recall the triangle - side - angle relationship

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

Step2: Compare the angles

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

Step3: Determine the side lengths

The side opposite \(\angle G\) is \(HJ\), the side opposite \(\angle J\) is \(GH\), and the side opposite \(\angle H\) is \(GJ\). So, the order of side lengths from longest to shortest is \(HJ\), \(GH\), and \(GJ\) (because of the side - angle relationship in a triangle: longer angle \(\Rightarrow\) longer opposite side)

Answer:

HJ, GH, and GJ