Question

list the side lengths of $\triangle wxy$ in order from shortest to longest.

Explanation:

Step1: Solve for s using angle sum

The sum of interior angles in a triangle is $180^\circ$.
$$39s + 74 + (s+66) = 180$$
$$40s + 140 = 180$$
$$40s = 40$$
$$s = 1$$

Step2: Calculate each angle

Find $\angle W$: $39s = 39(1) = 39^\circ$
Find $\angle Y$: $s+66 = 1+66 = 67^\circ$
$\angle X = 74^\circ$
Order of angles: $39^\circ < 67^\circ < 74^\circ$ (or $\angle W < \angle Y < \angle X$)

Step3: Match sides to opposite angles

In a triangle, the shortest side is opposite the smallest angle, and the longest side is opposite the largest angle:

• Side opposite $\angle W$: $XY$
• Side opposite $\angle Y$: $WX$
• Side opposite $\angle X$: $WY$

Answer:

$XY < WX < WY$