Which one of the following equations is not true for every acute triangle DEF?

[DW Student]

a) d Sin E = e Sin F

b) Sin D/Sin E = d/e

c) d(sin F) / f(sin D) = 1

d) sin E/e = sin F/f

 

[DW Student]

by d SIn E = e Sin F I meant d(Sin E) = e(Sin F)
Pls help and thanks

 

[Dr.Peterson]

Which one of the following equations is not true for every acute triangle DEF?

a) d Sin E = e Sin F

b) Sin D/Sin E = d/e

c) d(sin F) / f(sin D) = 1

d) sin E/e = sin F/f

I presume you are following the traditional labeling of a right triangle so that side d is opposite angle D, and so on.

Try rearranging each equation into a form like the Law of Sines, in whatever for you were taught. (There are several ways it can be stated.) Then look for ways each is different from the LOS. One will be different enough to be false.

 

[DW Student]

Yes sir, I chosed a) for this question because since sin E/e = sin F/f so it should be in similar form as f (sin E) = e (Sin f) but it has a) has a extra d in it. Therefore a) is the false statement .
Thank you for responding

 

[Dr.Peterson]

Yes sir, I chosed a) for this question because since sin E/e = sin F/f so it should be in similar form as f (sin E) = e (Sin f) but it has a) has a extra d in it. Therefore a) is the false statement .
Thank you for responding

Right. The Law of Sines relates two angles and their opposite sides; (a) is equivalent to sin E/e = sin F/d, which is wrong.