The value of tan(Q) = 3/4, given that ΔQRS ~ ΔXYZ. Computed using properties of similar triangles. Hence, the second option is the best choice.
According to the properties of similar triangle, the corresponding sides of similar triangles are in proportion.
In the question, we are given that ΔQRS ~ ΔXYZ.
By properties of similar triangles, we know that:
QR/XY = RS/YZ = SQ/ZX.
From this, we can show that:
RS/SQ = YZ/ZX ...(i).
We are asked to find the value of tan(Q).
By trigonometric ratios, we know that:
tan(Q) = Perpendicular/Base = RS/SQ.
From (i), we know that RS/SQ = YZ/ZX.
From figure, we know that YZ = 9, and ZX = 12.
Thus, YZ/ZX = 9/12 = 3/4.
Thus, tan(Q) = RS/SQ = YZ/ZX = 3/4.
Hence, the value of tan(Q) = 3/4, given that ΔQRS ~ ΔXYZ. Computed using properties of similar triangles. Hence, the second option is the best choice.
The question is incomplete. The complete question can be seen in the figure.
Learn more about similar triangles at
https://brainly.com/question/11920446
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