Question

consider △xyz
what are the ratios of sine, cosine, and tangent for angle y?
○ $\sin(y) = \frac{xz}{xy}$; $\cos(y) = \frac{yz}{xz}$; $\tan(y) = \frac{yz}{xy}$
○ $\sin(y) = \frac{xy}{xz}$; $\cos(y) = \frac{xz}{xy}$; $\tan(y) = \frac{yz}{xz}$
○ $\sin(y) = \frac{xz}{xy}$; $\cos(y) = \frac{yz}{xy}$; $\tan(y) = \frac{xz}{yz}$
○ $\sin(y) = \frac{yz}{xy}$; $\cos(y) = \frac{xz}{xy}$; $\tan(y) = \frac{xz}{yz}$

Explanation:

Step1: Identify sides for angle Y

In right $\triangle XYZ$ (right angle at Z):

• Hypotenuse: $XY$
• Opposite to $\angle Y$: $XZ$
• Adjacent to $\angle Y$: $YZ$

Step2: Calculate $\sin(Y)$

Sine = Opposite/Hypotenuse
$\sin(Y) = \frac{XZ}{XY}$

Step3: Calculate $\cos(Y)$

Cosine = Adjacent/Hypotenuse
$\cos(Y) = \frac{YZ}{XY}$

Step4: Calculate $\tan(Y)$

Tangent = Opposite/Adjacent
$\tan(Y) = \frac{XZ}{YZ}$

Answer:

$\sin(Y)=\frac{XZ}{XY};\cos(Y)=\frac{YZ}{XY};\tan(Y)=\frac{XZ}{YZ}$ (the third option)