Question

which side is the long leg in this 30 - 60 - 90 triangle?

Explanation:

Step1: Recall 30 - 60 - 90 triangle properties

In a 30 - 60 - 90 triangle, the sides are in the ratio \(1:\sqrt{3}:2\). The side opposite the 30° angle is the short leg, the side opposite the 60° angle is the long leg, and the side opposite the 90° angle is the hypotenuse.

Step2: Identify the angles and their opposite sides

The side of length 4 is opposite the 30° angle (since the right - angle is 90°, and the other non - right angle is 60°, the side adjacent to the 60° angle and opposite the 30° angle is the short leg). The side labeled \(v\) is opposite the 60° angle.

Answer:

\(v\)