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Before I catch up on the 32 hours of sleep I have missed...

 

In right triangle ABC with angle B = 90 degrees, we have 2 sin A = 3 cos A.  What is sin A?

 

Thanks!

 Jun 21, 2018
 #1
avatar+98042 
+2

2 sin A  = 3 cos A     square both sides

 

4 sin^2 A  = 9 cos^2 A

 

4 sin^2 A = 9 [ 1 - sin^2 A]

 

4 sin ^2 A  = 9 - 9 sin^2 A     rearrange as

 

13 sin^2 A    = 9

 

sin^2 A  = 9 /13       sinc A is acute and  < 90°   ...take the positive root

 

sin A  = 3 / √13   =  ( 3 √13 ) / 13

 

 

cool cool cool

 Jun 21, 2018
 #2
avatar+1442 
+2

Thanks CPhill!

AnonymousConfusedGuy  Jun 21, 2018

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