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In triangle XYZ, we have ngle X = 90 degrees and tan Z = 7. If YZ = 100, then what is XY?

 Mar 24, 2020
 #1
avatar+111330 
+1

Y

 

X                Z

 

Mmmm.....let's see

 

YZ  = 100

 

If the tan Z = 7

 

This indicates  that    XY / XZ =   7

 

So    this implies that    XY =  7XZ  ⇒   XY/7  = XZ

 

So....using the Pythagorean Theorem we know that

 

YZ  = √  [ XY^2  + XZ^2]        subbing, we have  that

 

100   = √ [ XY^2  + (XY/7)^2 ]    simplify

 

100 = √  [XY^2  +  XY^2 / 49 ]

 

100  =  √ [ 49XY^2 + XY^2 ]   / 7        multiply both sides  by 7

 

700 = √]50 XY^2]      square both sides

 

490000 = 50 XY^2     divide both sides by  50

 

9800 =  XY^2     take the positive root

 

XY =  √9800  = √[4900 * 2  ] =  70√​2

 

 

 

cool cool cool

 Mar 24, 2020
 #2
avatar+1970 
+2

Awesome, CPhill!

CalTheGreat  Mar 24, 2020

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