List the side lengths from shortest to longest for each triangle.

Steps to Solve

1. Triangle a: Find the missing angle

The sum of the angles in a triangle is 180 degrees. Let the missing angle be $x$. $$ 47 + 35 + x = 180 $$ $$ 82 + x = 180 $$ $$ x = 180 - 82 = 98 $$ So, the angles are $35^\circ$, $47^\circ$, and $98^\circ$.

2. Triangle a: Order the side lengths

The side opposite the largest angle is the longest, and the side opposite the smallest angle is the shortest. The angles in increasing order are $35^\circ$, $47^\circ$, $98^\circ$. The sides opposite these angles are $y$, $z$, and $x$, respectively. Therefore, the side lengths from shortest to longest are $y, z, x$.

3. Triangle b: Find the missing angle

The sum of the angles in a triangle is 180 degrees. Let the missing angle be $x$. $$ 88 + 52 + x = 180 $$ $$ 140 + x = 180 $$ $$ x = 180 - 140 = 40 $$ So, the angles are $40^\circ$, $52^\circ$, and $88^\circ$.

4. Triangle b: Order the side lengths

The angles in increasing order are $40^\circ$, $52^\circ$, $88^\circ$. The sides opposite these angles are $m$, $l$, and $n$, respectively. Therefore, the side lengths from shortest to longest are $m, l, n$.

5. Triangle c: Find the missing angle

The sum of the angles in a triangle is 180 degrees. Let the missing angle be $x$. $$ 45 + 50 + x = 180 $$ $$ 95 + x = 180 $$ $$ x = 180 - 95 = 85 $$ So, the angles are $45^\circ$, $50^\circ$, and $85^\circ$.

6. Triangle c: Order the side lengths

The angles in increasing order are $45^\circ$, $50^\circ$, $85^\circ$. The sides opposite these angles are $f$, $e$, and $d$, respectively. Therefore, the side lengths from shortest to longest are $f, e, d$.