Question

trigonometric ratios
given right triangle xyz, which correctly describes the locations of the sides in relation to ∠y?
(options:

1. a is adjacent, b is opposite, c is the hypotenuse
2. a is opposite, b is adjacent, c is the hypotenuse
3. a is the hypotenuse, b is opposite, c is adjacent
4. a is adjacent, b is the hypotenuse, c is opposite

)
(image of right triangle xyz with right angle at z, sides labeled a (yz), b (xz), c (xy))

Explanation:

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

• The hypotenuse is the side opposite the right angle. In \(\triangle XYZ\), the right angle is at \(Z\), so the hypotenuse is \(XY\) (length \(c\)).
• For an acute angle (here \(\angle Y\)), the adjacent side is the side that forms the angle along with the hypotenuse. So, the side adjacent to \(\angle Y\) is \(YZ\) (length \(a\)) because it is one of the sides that make up \(\angle Y\) (the other being the hypotenuse \(XY\)).
• The opposite side is the side that does not form the angle and is opposite to the angle. So, the side opposite to \(\angle Y\) is \(XZ\) (length \(b\)) as it is across from \(\angle Y\).

So, \(a\) ( \(YZ\)) is adjacent to \(\angle Y\), \(b\) ( \(XZ\)) is opposite to \(\angle Y\), and \(c\) ( \(XY\)) is the hypotenuse.

Answer:

The correct description is "a is adjacent, b is opposite, c is the hypotenuse" (assuming this is one of the options, for example, if the first option is "a is adjacent, b is opposite, c is the hypotenuse", then the answer is that option).