Question

\\(\delta abc\\) has the following angle measurements:

\\(\angle a = 45^\circ\\)
\\(\angle b = 60^\circ\\)
\\(\angle c = 75^\circ\\)

which of the following is the largest side of this triangle?

• \\(\overline{bc}\\)
• \\(\overline{ab}\\)
• \\(\overline{cb}\\)
• \\(\overline{ac}\\)

Explanation:

Identify the given angle measurements

We are given the interior angles of \(\triangle ABC\):

$$
LATEXBLOCK0
$$

Determine the largest angle

Comparing the angle measures:

$$ 75^\circ > 60^\circ > 45^\circ $$

Thus, \(\angle C\) is the largest angle.

Apply the angle-side relationship

In any triangle, the longest side is always opposite the largest angle.

• The side opposite to \(\angle A\) is \(\overline{BC}\).
• The side opposite to \(\angle B\) is \(\overline{AC}\).
• The side opposite to \(\angle C\) is \(\overline{AB}\).

Since \(\angle C\) is the largest angle, the opposite side \(\overline{AB}\) must be the longest side.

Answer:

• (A) \(\overline{BC}\)
• (B) \(\overline{AB}\) (Correct answer)
• (C) \(\overline{CB}\)
• (D) \(\overline{AC}\)