+289 In triangle $XYZ$, we have $\angle Z = 90^\circ$, $XY = 10$, and $YZ = \sqrt{51}$. What is $\tan X$?
+1632 Triangle XYZ is a right triangle because one of its angles is 90 degrees. XY is the hypotenuse because it is the line segment opposite the right angle. Using the pythagorean theorem, XY^2 - YZ^2 = XZ^2. 100 - 51 = 49. So XZ = 7.
Because tan (tangents) for a right triangle takes the ratio of the adjacent side to the angle to the hypotenuse, then we get the adjacent side as XZ and the hypotenuse as XY. XZ / XY = 7 / 10.
Thus, \(\tan x = {7\over10}\). 
+1694 Who did give you 2 ++ for the wrong answer? Read the question again.
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Angle Z = 90º XY = 10 YZ = √51 XZ = 7 (correct)
XY => hypotenuse YZ => opposite XZ => adjacent
tan(X) = opposite / adjacent
tan(X) = √51 / 7
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btw... 7 / 10 = sin(Y)
