Question

in $\triangle hij$, $mangle h = 43^{circ}$ and $mangle i = 104^{circ}$. which statement about the sides of $\triangle hij$ must be true? answer ij > hi > jh hi > ij > jh jh > hi > ij jh > ij > hi hi > jh > ij ij > jh > hi submit answer

Explanation:

Step1: Find the measure of angle J

The sum of angles in a triangle is 180°. So, $m\angle J=180^{\circ}-(m\angle H + m\angle I)=180^{\circ}-(43^{\circ}+ 104^{\circ}) = 33^{\circ}$.

Step2: Recall the angle - side relationship

In a triangle, the longest side is opposite the largest angle and the shortest side is opposite the smallest angle. Since $m\angle I>m\angle H>m\angle J$, the side opposite $\angle I$ is the longest, the side opposite $\angle H$ is the second - longest, and the side opposite $\angle J$ is the shortest. The side opposite $\angle I$ is $HJ$, the side opposite $\angle H$ is $IJ$, and the side opposite $\angle J$ is $HI$. So, $HJ> IJ> HI$. But looking at the options in terms of the given labels, the correct order of sides is $IJ> HI> JH$.

Answer:

IJ > HI > JH