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:

To determine the sides relative to ∠Y in right triangle XYZ (right - angled at Z):

1. Hypotenuse: The hypotenuse is the side opposite the right angle. In triangle XYZ, the right angle is at Z, so side \( c \) (XY) is the hypotenuse as it is opposite ∠Z.
2. Adjacent side to ∠Y: The adjacent side to an angle in a right - triangle is the non - hypotenuse side that forms the angle with the hypotenuse. For ∠Y, side \( a \) (YZ) forms ∠Y along with the hypotenuse \( c \), so \( a \) is adjacent to ∠Y.
3. Opposite side to ∠Y: The opposite side to an angle is the side that does not form the angle. For ∠Y, side \( b \) (XZ) does not form ∠Y, so \( b \) is opposite to ∠Y.

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

Answer:

D. a is adjacent, b is opposite, c is the hypotenuse