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In triangle XYZ, \angleY = 45^\circ and \angleZ = 60^\circ. If XZ  = 4, then what is XY?
 

 Dec 26, 2020
 #1
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By the Sine Law, XY = 3 - sqrt(3).

 Dec 26, 2020
 #2
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We have that

 

XY/ sin Z  = XZ / sin Y

 

XY/ sin 60°  = 4 /  sin 45°

 

XY  =  4sin 60°  /sin 45°

 

XY  =  4 sqrt (3)  / sqrt (2)

 

XY =  4 sqrt (6)  / 2  =   2sqrt (6)

 

 

cool cool cool

 Dec 26, 2020
 #3
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In triangle XYZ, \angleY = 45^\circ and \angleZ = 60^\circ. If XZ  = 4, then what is XY?

 

XY / XZ = sin(∠X) / sin(∠Y)

 

XY = 2√6

 Dec 26, 2020

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