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In triangle ABC, CA = 4sqrt2, CB = 4sqrt3, and angle A = 45 degrees. What is B in degrees?

 Nov 30, 2020
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  CA  = b =  side opposite angle B

 CB  = a = side opposite angle A

 

Using the Law of Sines

 

sin B / b =  sin A / a

 

sin B / (4sqrt (2) )  = sin A  / (4sqrt (3))

 

sin B  /  (4 sqrt (2))  =  sin 45° / (4sqrt (3))

 

sin B  / (4sqrt (2))  = (1/sqrt (2) )  / (4sqrt (3))

 

sin B =  (4sqrt (2) ) / (4sqrt (3))  * (1 /sqrt (2) )

 

sin B   =    1/ sqrt (3)

 

arcsin (1/sqrt (3))  = B ≈   35.26°

 

 

cool cool cool

 Nov 30, 2020

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