Question

triangle inequalities
choose the word that correctly completes the statement.
since angle b is the largest angle, \\(\overline{ac}\\) is the \underline{\quad\quad} side.
adjacent, included, shortest, longest
(image of triangle abc with angles at a: 60°, at b: 75°, at c: 45°)

Explanation:

Step1: Recall the triangle side - angle relationship

In a triangle, the largest angle is opposite the longest side, and the smallest angle is opposite the shortest side. This is a fundamental property of triangles in the subfield of Geometry (under Mathematics).

Step2: Identify the angle opposite to side \(AC\)

In triangle \(ABC\), side \(AC\) is opposite angle \(B\). We are given that angle \(B = 75^{\circ}\), angle \(A=60^{\circ}\) and angle \(C = 45^{\circ}\). So angle \(B\) is the largest angle among the three angles of the triangle.

Step3: Determine the type of side \(AC\)

Since angle \(B\) (the largest angle) is opposite side \(AC\), by the side - angle relationship in a triangle, the side opposite the largest angle is the longest side. So side \(AC\) is the longest side.

Answer:

longest