Question

list the sides of the triangle in order from shortest to longest. note that the figure is not drawn to scale.

Explanation:

Step1: Find the measure of angle \( L \)

The sum of angles in a triangle is \( 180^{\circ} \). Let \( \angle L=x \). Then \( x + 57^{\circ}+33^{\circ}=180^{\circ} \). So \( x=180^{\circ}-(57^{\circ} + 33^{\circ})=90^{\circ} \).

Step2: Recall the side - angle relationship in a triangle

In a triangle, the side opposite the smaller angle is shorter. The side opposite \( 33^{\circ}\) (side \( LK\)), the side opposite \( 57^{\circ}\) (side \( LM\)), and the side opposite \( 90^{\circ}\) (side \( KM\)).

Answer:

\( LK\lt LM\lt KM \)