Right Triangle X Y Z has a right angle labeled upper Y. The side across from angle upper X is side x, the side across from angle upper Y is side y, and the side across from angle upper Z is side z.

Question

Question
Use the triangle to answer the question.
What is the tangent of angle Z?
(1 point)
Responses

tangent upper Z equals Start Fraction y over x End Fraction
Image with alt text: tangent upper Z equals Start Fraction y over x End Fraction

tangent upper Z equals Start Fraction x over z End Fraction
Image with alt text: tangent upper Z equals Start Fraction x over z End Fraction

tangent upper Z equals Start Fraction z over x End Fraction
Image with alt text: tangent upper Z equals Start Fraction z over x End Fraction

tangent upper Z equals Start Fraction z over y End Fraction

Answer 1

In a right triangle, the tangent of an angle is defined as the ratio of the length of the opposite side to the length of the adjacent side.

For triangle XYZ:

• The side opposite angle Z is side y (since Y is the right angle).
• The side adjacent to angle Z is side x.

Thus, the tangent of angle Z can be expressed as:

$$\tan (Z)=\frac{\text{opposite}}{\text{adjacent}}=\frac{y}{x}.$$

So the correct response is:

tangent upper Z equals Start Fraction y over x End Fraction