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Question

Feature
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
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
Image with alt text: tangent upper Z equals Start Fraction z over y End Fraction
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Answer 1

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

In triangle XYZ:

• Angle Y is the right angle.
• The side opposite angle Z is side y.
• The side adjacent to angle Z is side x.

Therefore, 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.