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Select the correct answer.

A building has a triangular rooftop terrace which is modeled by triangle ABC. In triangle ABC, the measure of angle A is 55 degrees, the measure of angle B is 65 degrees, and the measure of angle C is 60 degrees.

Which side of the terrace has the greatest length?

A. Cannot be determined
B. line segment AC
C. line segment AB
D. line segment BC

User Icon for Bot GPT-4o Bot GPT-4o answered
3 months ago

In a triangle, the length of a side is directly related to the measure of the angle opposite to it. The greater the angle, the longer the side opposite to that angle.

For triangle ABC:
- Angle A = 55 degrees
- Angle B = 65 degrees
- Angle C = 60 degrees

The side lengths are opposite to these angles:
- Side BC is opposite to angle A (55 degrees)
- Side AC is opposite to angle B (65 degrees)
- Side AB is opposite to angle C (60 degrees)

Since angle B (65 degrees) is the largest angle, the side opposite to angle B, which is side AC, will have the greatest length.

Therefore, the correct answer is:

B. line segment AC