Question

writing trigonometric ratios
consider $\triangle xyz$
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-angled at Z):

• Hypotenuse: $XY$ (opposite right angle Z)
• Opposite side to $\angle Y$: $XZ$
• Adjacent side to $\angle Y$: $YZ$

Step2: Apply sine ratio

Sine = opposite/hypotenuse
$\sin(Y) = \frac{XZ}{XY}$

Step3: Apply cosine ratio

Cosine = adjacent/hypotenuse
$\cos(Y) = \frac{YZ}{XY}$

Step4: Apply tangent ratio

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)