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# Geometry

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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

Apr 20, 2022
#2
+2440
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That question is different than this one...

BuilderBoi  Apr 20, 2022
#3
+2440
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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