Identify Adjacent Side to Angle Q in Right Triangle HNQ

Understand the request: The question asks to identify the segment adjacent to angle ( ) in the given right-angled triangle .

Define “adjacent side” in a triangle: In any angle of a triangle, the sides that form that angle are called the adjacent sides (or legs, if it’s a right triangle). The side opposite the angle is called the opposite side, and the side opposite the right angle is the hypotenuse.

Identify the angle of interest: We are focused on .

Identify the sides connected to : The angle is formed by the intersection of two line segments:

Analyze the options provided: The choices are:

Select the correct adjacent segment(s): Both and are adjacent to . In the context of trigonometric definitions (SOH CAH TOA) applied to acute angles in a right triangle, the term “adjacent side” usually refers to the leg adjacent to the angle, excluding the hypotenuse, unless the question intends to include the hypotenuse.

If we consider the standard trigonometric roles relative to :

Since is listed as an option and is unambiguously an adjacent leg, it is the intended answer, representing the side adjacent to that is not the hypotenuse.

Conclusion: The segment forms and is one of the legs adjacent to it.