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?

• cannot be determined
• \\(\overline{ac}\\)
• \\(\overline{bc}\\)
• \\(\overline{ab}\\)

Explanation:

Identify the given angle measures

Using the Angle-Side Relationships knowledge point

$$
LATEXBLOCK0
$$

Order the angle measures from greatest to least

Using the Angle-Side Relationships knowledge point

$$ 65^\circ > 60^\circ > 55^\circ \implies m\angle B > m\angle C > m\angle A $$

Determine the corresponding opposite sides

Using the Angle-Side Relationships knowledge point

$$
LATEXBLOCK1
$$

Apply the theorem to find the longest side

Using the Angle-Side Relationships knowledge point

$$ m\angle B > m\angle C > m\angle A \implies AC > AB > BC $$

Answer:

• (A) Cannot be determined
• (B) \(\overline{AC}\) (Correct answer)
• (C) \(\overline{BC}\)
• (D) \(\overline{AB}\)