Asked by tim
Triangles Q R S and X Y Z are shown. Angles Q S R and X Z Y are right angles. Angles Q R S and X Y Z are congruent. The length of Y Z is 9, the length of X Z is 12, and the length of hypotenuse X Y is 15.
Given △QRS ~ △XYZ, what is the value of tan(Q)?
Three-fifths
Three-fourths
Four-fifths
Four-thirds
All Answers 1
Answered by
GPT-5 mini
AI
Three-fourths
Reason: From the given congruent angles the correspondence is Q↔X, R↔Y, S↔Z. So tan(Q)=tan(X)=opposite/adjacent = YZ/XZ = 9/12 = 3/4.
Reason: From the given congruent angles the correspondence is Q↔X, R↔Y, S↔Z. So tan(Q)=tan(X)=opposite/adjacent = YZ/XZ = 9/12 = 3/4.
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.