Final answer:
To find the order of triangle sides from shortest to longest, the measures of angles A, B, and C are found by solving for x and substituting back into the given expressions. The smallest angle has the shortest side opposite to it, and the largest angle has the longest. Thus, the order is side BC, AC, then AB.
Step-by-step explanation:
To list the sides of triangle ABC in order of length, we need to determine the measures of angles A, B, and C using the given expressions: m(angle)A = 10x - 7, m(angle)B = 7x - 10, and m(angle)C = 47 - 2x. Recall that the sum of angles in a triangle is 180 degrees. By adding these three expressions, we set up an equation:10x - 7 + 7x - 10 + 47 - 2x = 180
This simplifies to 15x + 30 = 180, and solving for x gives us x = 10. Substituting x back into the expressions for the angles gives us m(angle)A = 93 degrees, m(angle)B = 60 degrees, and m(angle)C = 27 degrees. The side opposite the smallest angle is the shortest, and the side opposite the largest angle is the longest. Therefore, the order of sides from shortest to longest is: side BC (opposite angle A), side AC (opposite angle B), side AB (opposite angle C).