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[asy] unitsize(1.5 cm);pair A,B,C;A=(0,0);B=(5,0);C=(1,1);draw(A--B--C--A);label(

 

Find AB

 Apr 11, 2022
 #1
avatar+122390 
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Note that angle C  = 180  - 45 - 15  =  120

 

Using the Law of Sines

 

12/ sin 45   = AB  /sin 120

 

12  / ( 1/sqrt 2)  = AB / (sqrt (3) / 2)

 

(12 sqrt 2) * (sqrt (3) / 2)  = AB

 

12 sqrt 3  / sqrt 2  = AB

 

12 sqrt (2) sqrt (3)  / 2   =  AB

 

6 *sqrt 6   = AB

 

cool cool cool

 Apr 11, 2022

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