Question

practice relating the side lengths and angle measures of one or two triangles. 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 angle, the opposite side, jh, is. the order of the side lengths from longest to shortest is.

Explanation:

Step1: Analyze angle G's type

Angle G is \(110^\circ\), which is greater than \(90^\circ\), so it's an obtuse angle.

Step2: Relate angle to opposite side

In a triangle, the larger the angle, the longer its opposite side. Since angle G is the largest angle (\(110^\circ > 40^\circ > 30^\circ\)), its opposite side JH is the longest side.

Step3: Order angles by measure

Angles: \( \angle G = 110^\circ\), \( \angle J = 40^\circ\), \( \angle H = 30^\circ\). So \( \angle G > \angle J > \angle H\).

Step4: Order sides by opposite angles

Opposite sides: \(JH\) (opposite \( \angle G\)), \(GH\) (opposite \( \angle J\)), \(GJ\) (opposite \( \angle H\)). So side lengths from longest to shortest: \(JH > GH > GJ\).

Answer:

1. Since angle G is \(\boldsymbol{\text{obtuse}}\) angle, the opposite side, JH, is \(\boldsymbol{\text{the longest}}\).
2. The order of the side lengths from longest to shortest is \(\boldsymbol{JH, GH, GJ}\).