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+8
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avatar+258 

In triangle $XYZ$, we have $\angle Z = 90^\circ$, $XY = 10$, and $YZ = \sqrt{51}$. What is $\tan X$?

 Feb 8, 2022
 #1
avatar+516 
0

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, \(\tan x = {7\over10}\)smiley

 Feb 8, 2022
 #2
avatar+1696 
+3

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)

civonamzuk  Feb 8, 2022
edited by Guest  Feb 8, 2022

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