Question

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 ^ { \circ } \\), the measure of \\( \angle b \\) is \\( 65 ^ { \circ } \\), and the measure of \\( \angle c \\) is \\( 60 ^ { \circ } \\).
which side of the terrace has the greatest length?
a. cannot be determined
b. \\( \overline { a c } \\)
c. \\( \overline { a b } \\)
d. \\( \overline { b c } \\)

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

We have \(\angle A = 55^{\circ}\), \(\angle B=65^{\circ}\), \(\angle C = 60^{\circ}\). 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:

B. \(\overline{AC}\)