Question 1059132: Determine the number of possible triangles that can be draw based on the given information:
In triangle DEF, angle D = 66 degrees; d = 15 cm; and f = 11 cm
I would really appreciate some help with this question.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! i believe this has to do with the law of sines.
that law says that a / sin(A) = b / sin(B) = c / sin(C).
this can also be written as d / sin(D) = e / sin(E) = f / sin(F)
your triangle is DEF.
side opposite angle D is d.
side opposite angle E is e.
side opposite angle F is f.
you are given that angle D is equal to 66 degrees and side d is equal to 15 and side f is equal to 11.
by the law of sines, you get d / sin(D) = f / sin(F).
this becomes 15 / sin(66) = 11 / sin(F)
solve for sin(F) to get sin(F) = 11 * sin(66) / 15
solve for sin(F) to get sin(F) = .6699333356
solve for F to get F = arcsin(.6699333356) = 42.06191982 degrees.
since the sum of angle D and F is less than 180, then at least 1 triangle is possible.
to see if a second trianlge is possible, take 180 - 42.06191982 degrees to get 137.9380802 degrees.
add that to 66 degrees and the sum is greater than 180, so only 1 triangle is possible.
here's a reference that might help you to understand.
http://www.regentsprep.org/regents/math/algtrig/att12/lawofsinesAmbiguous.htm
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