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In triangle XYZ, we have angle X = 90 and tan Y = 3/2. If YZ = 80, then what is XY?

 Jul 20, 2022
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Y

        80

X            Z

 

tan Y  =  3/2  = XZ / XY    then  XZ =  (3/2)XY

 

So

 

(XY)^2  + [(3/2) XY]^2  = 80^2

 

XY^2  + (9/4)XY^2  = 6400

 

(13/4)XY^2  =  6400

 

XY^2  =   6400 ( 4 /13)

 

XY^2  =  (6400 * 4)  / 13

 

XY  = 80 * 2   / sqrt (13)

 

XY  =  160/ sqrt (13)  

 

cool cool cool

 Jul 20, 2022

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