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Trigonometry Question (Triangles)?
Um so my other question got deleted ? Whatever.
So I reallyyy don't understand how to find the solutions to a triangle. Here's the question:
Find the solutions of triangle RST when r = 13, S = 140 degrees, and s = 10
I drew out a triangle, and I know that I need to find the last side to be able to use the law of cosine. I just dont understand when to use sine, cosine, or tangent to find the last side.
Help me out, I'd appreciate it.
1 Answer
- Anonymous1 decade agoFavorite Answer
The triangle isn't a right triangle, so you will need to stick with either the Law of Sines or the Law of Cosines.
You can actually see that there are no solutions to this already since r > s, we have that R > S ==> R > 140°. However, since there can be at most one obtuse angle in a triangle, no solutions exist.
Alternatively, since you are given a SAS case, you will need to use the Law of Sines. We have:
sin(R)/r = sin(S)/s
==> sin(R)/13 = sin(140°)/10, since r = 13, S = 140°, and s = 10
==> sin(R) = (13/10)sin(140°)
==> R ≈ 57° or R ≈ 123°.
However, since R + S > 180° for both values of R, again, there are no solutions to this triangle.
I hope this helps!