Question

given right triangle xyz, which correctly describes the locations of the sides in relation to ∠y?

• a is opposite, b is adjacent, c is the hypotenuse
• a is the hypotenuse, b is opposite, c is adjacent
• a is adjacent, b is the hypotenuse, c is opposite
• a is adjacent, b is opposite, c is the hypotenuse

Explanation:

Step1: Recall triangle side definitions

In a right - triangle, the hypotenuse is the side opposite the right angle. For an angle (here \(\angle Y\)), the adjacent side is the non - hypotenuse side that forms the angle with the hypotenuse, and the opposite side is the non - hypotenuse side that does not form the angle.

Step2: Analyze each side

In right - triangle \(XYZ\) with right angle at \(Z\):

• Side \(a\) forms \(\angle Y\) along with the hypotenuse \(c\), so \(a\) is adjacent to \(\angle Y\).
• Side \(b\) does not form \(\angle Y\), so \(b\) is opposite to \(\angle Y\).
• Side \(c\) is the hypotenuse (opposite the right angle).

Answer:

\(a\) is adjacent, \(b\) is opposite, \(c\) is the hypotenuse.