Question

list the sides of each triangle in order from shortest to longest.
\t δmkl with ∠m = 65°, ∠k = 56°, and ∠l = 59°
\t
\t
\t choose the correct order of the sides from shortest to longest.
\t
\t
\t a. –lk, –lm, –mk
\t
\t b. –lm, –mk, –lk
\t
\t c. –lk, –mk, –lm
\t
\t d. –lm, –lk, –mk
\t
\t e. –mk, –lk, –lm
\t
\t f. –mk, –lm, –lk

Explanation:

Step1: Compare the angles

In a triangle, the larger the angle, the longer the side opposite it.
We have \(\angle K = 56^{\circ}\), \(\angle L=59^{\circ}\), \(\angle M = 65^{\circ}\). So, \(\angle K<\angle L<\angle M\).

Step2: Identify the sides opposite the angles

Side opposite \(\angle K\) is \(\overline{LM}\), side opposite \(\angle L\) is \(\overline{MK}\), side opposite \(\angle M\) is \(\overline{LK}\).
Since \(\angle K<\angle L<\angle M\), then \(\overline{LM}<\overline{MK}<\overline{LK}\)

Answer:

B. \(\overline{LM},\overline{MK},\overline{LK}\)