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In right triangle DEF, we have angle E = 90 degrees and tan D = 3*sin D. What is sin F?

 

Super confused about this one, thanks!

 Jun 21, 2018
 #1
avatar+101345 
+2

In right triangle DEF, we have angle E = 90 degrees and tan D = 3*sin D. What is sin F?

 

tan D  = 3 sin D

 

sin D  / cos D  =   3 sin D        

 

Since  0° < D < 90°, then sin D  >  0

 

So...divide both sides by sin D and we have that

 

1 / cos D  = 3  .......rearrange as

 

cos D   = 1/3

 

Since D and F  are  complementary, then

 

cos D  = 1/3  =  sin  F

 

 

cool cool cool

 Jun 21, 2018
 #2
avatar+1438 
+2

Great thank you so much!

AnonymousConfusedGuy  Jun 21, 2018

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