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In triangle ABC, CA=4sqrt(2), CB=4sqrt(3), and A=\(45\) degrees. What is B in degrees?

 Apr 20, 2022
 #1
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\(45\) degrees

 

Explanation: https://web2.0calc.com/questions/help-please_11085

 Apr 20, 2022
 #2
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That question is different than this one...

BuilderBoi  Apr 20, 2022
 #3
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Draw altitude \(CM\).

 

We know that \(\triangle ACM = 45-45-90\).

 

Thus, \(CM = AM = 4\).

 

In \(\triangle CBM\), we know that \(CB = 4\sqrt3\) and \(CM = 4\)

 

We can form the equation: \(\sin(B) = {\sqrt3 \over 3}\)

 

Taking the inverse, we find that \(\color{brown}\boxed {B \approx 35.264}\)

 

Here is the diagram: 

 Apr 20, 2022
edited by BuilderBoi  Apr 20, 2022

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