Final answer:
To determine the longest side in triangle ABC, solve the equation to find the value of x, and substitute it into the expressions for angles B and C. Then compare the lengths of the sides AB, BC, and AC.
Step-by-step explanation:
To determine which side is the longest in triangle ABC, we need to compare the lengths of the sides. Let's start by finding the values of angles B and C in terms of x. Given that m∠B = (3x - 2)° and m∠C = (2x + 7)°, we can set up an equation: m∠A + m∠B + m∠C = 180°. Substituting the given values, we have 60° + (3x - 2)° + (2x + 7)° = 180°. Solving this equation will give us the value of x. Once we have the value of x, we can substitute it back into the expressions for angle B and C and calculate their values. Finally, we can compare the lengths of the sides AB, BC, and AC to determine which side is the longest.