Question

select the correct answer.
a building has a triangular rooftop terrace which is modeled by triangle abc. in triangle abc, the measure of ∠a is 55°, the measure of ∠b is 65°, and the measure of ∠c is 60°.
which side of the terrace has the greatest length?
○ a. (overline {ac})
○ b. cannot be determined
○ c. (overline {bc})
○ d. (overline {ab})

Explanation:

Step1: Recall the triangle side - angle relationship

In a triangle, the larger the angle, the longer the side opposite it.

Step2: Compare the angles

Given \(\angle A = 55^{\circ}\), \(\angle B=65^{\circ}\), \(\angle C = 60^{\circ}\). Since \(65^{\circ}>60^{\circ}>55^{\circ}\), so \(\angle B\) is the largest angle.

Step3: Identify the side opposite the largest angle

The side opposite \(\angle B\) is \(\overline{AC}\).

Answer:

A. \(\overline{AC}\)