Question

trigonometric ratios given right triangle xyz, which correctly describes the locations of the sides in relation to ∠y? a is the hypotenuse, b is opposite, c is adjacent a is adjacent, b is the hypotenuse, c is opposite a is opposite, b is adjacent, c is the hypotenuse a is adjacent, b is opposite, c is the hypotenuse

Explanation:

Step1: Recall right triangle terms

In a right triangle, hypotenuse is opposite right angle. For an acute angle (here $\angle Y$), adjacent side is next to the angle (shares the angle), opposite side is across from the angle.

• Right angle at $Z$, so hypotenuse is $c$ (side $XY$).
• For $\angle Y$:
• Adjacent side: shares $\angle Y$ (side $a$, $YZ$).
• Opposite side: across from $\angle Y$ (side $b$, $XZ$).
• Hypotenuse: $c$ (longest side, $XY$).

Step2: Match with options

Check each option:

• Option 1: Wrong (a not hypotenuse).
• Option 2: Wrong (b not hypotenuse).
• Option 3: Wrong (a and b labels reversed).
• Option 4: Correct (a adjacent, b opposite, c hypotenuse).

Answer:

a is adjacent, b is opposite, c is the hypotenuse (the fourth option)