consider △xyz\nwhat are the ratios of sine, cosine, and tangent for angle y?\n○ $\\sin(y) = \\frac{xz}{xy}$…

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

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

Answer

Explanation:

Step1: Recall Trigonometric Ratios

In a right - triangle, for an acute angle (\theta):

  • (\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}})
  • (\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}})
  • (\tan\theta=\frac{\text{opposite}}{\text{adjacent}})

In (\triangle XYZ) with right - angle at (Z), for angle (Y):

  • The side opposite to angle (Y) is (XZ).
  • The side adjacent to angle (Y) is (YZ).
  • The hypotenuse (the side opposite the right - angle) is (XY).

Step2: Calculate (\sin(Y))

Using the formula for sine, (\sin(Y)=\frac{\text{opposite to }Y}{\text{hypotenuse}}=\frac{XZ}{XY})

Step3: Calculate (\cos(Y))

Using the formula for cosine, (\cos(Y)=\frac{\text{adjacent to }Y}{\text{hypotenuse}}=\frac{YZ}{XY})

Step4: Calculate (\tan(Y))

Using the formula for tangent, (\tan(Y)=\frac{\text{opposite to }Y}{\text{adjacent to }Y}=\frac{XZ}{YZ})

Answer:

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