Question

c. without determining the actual value, what information do you know about x in the diagram at right?

Explanation:

Step1: Apply triangle side - angle relationship

In a triangle, the larger side is opposite the larger angle.

Step2: Analyze the angles

One angle is \(76^{\circ}\), and the right - angle is \(90^{\circ}\). So the third angle (opposite to side \(x\)) is \(180^{\circ}-90^{\circ} - 76^{\circ}=14^{\circ}\).
Since \(14^{\circ}<76^{\circ}<90^{\circ}\), and the side opposite to \(14^{\circ}\) is shorter than the side opposite to \(76^{\circ}\).

Answer:

\(x < 9\)