Question

list the sides of each triangle in order from shortest to longest.
\\( \delta k l m \\) with \\( \angle k = 77 ^ { \circ } \\), \\( \angle l = 43 ^ { \circ } \\), and \\( \angle m = 60 ^ { \circ } \\)

\\( \bigcirc \\) a. \\( \overline { k l } \\), \\( \overline { m l } \\), \\( \overline { m k } \\)
\\( \bigcirc \\) b. \\( \overline { k l } \\), \\( \overline { m k } \\), \\( \overline { m l } \\)
\\( \bigcirc \\) c. \\( \overline { m l } \\), \\( \overline { k l } \\), \\( \overline { m k } \\)
\\( \bigcirc \\) d. \\( \overline { m l } \\), \\( \overline { m k } \\), \\( \overline { k l } \\)
\\( \bigcirc \\) e. \\( \overline { m k } \\), \\( \overline { k l } \\), \\( \overline { m l } \\)
\\( \bigcirc \\) f. \\( \overline { m k } \\), \\( \overline { m l } \\), \\( \overline { k l } \\)

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 \(\angle L = 43^{\circ}\), \(\angle M=60^{\circ}\), \(\angle K = 77^{\circ}\). So, \(\angle L<\angle M<\angle K\).

Step3: Determine the sides opposite the angles

The side opposite \(\angle L\) is \(\overline{MK}\), the side opposite \(\angle M\) is \(\overline{KL}\), and the side opposite \(\angle K\) is \(\overline{ML}\).

Answer:

D. \(\overline{ML},\overline{MK},\overline{KL}\)