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# geo help! thanks

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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
+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

Mar 24, 2020
#2
+1970
+2

Awesome, CPhill!

CalTheGreat  Mar 24, 2020
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