Right-Triangle Geometry

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