Question

When you're given the side lengths and/or angle measures of a triangle, how do you know if it is:
(a. able to actually exist
(b. one or two triangles

?

Answer 1

As far as side lengths if the longest side is less than the sum of the other two sides the triangle can exist.
Here's a triangle tester:
http://1728.org/trianinq.htm

Answer 2

Do you know how I can determine a triangle based on trig functions? Like, in my notes it says that when adjacent>opposite>hypotenuse, there are two triangles, but I don't quite understand it.

Answer 3

@sunny9dragon Are you talking about the SSA, as known as the "Ambiguous Case?"

That is the one where you are given two sides and a non-included angle of a possible triangle. Zero, one, or two different triangles may exist based on the data.

Answer 4

Does the Ambiguous case only apply to SSA?

Answer 5

To my knowledge, the Ambiguous Case is based on SSA.

Read more here: http://www.regentsprep.org/regents/math/algtrig/ATT12/lawofsinesAmbiguous.htm

Answer 6

Just use the law of sines. It's a ratio system such that sin(angleA)/side a is equal to all other sides in the same way ie... = sin(angleB)/side b = sin(angle C)/ side c. Where the side is across from the angle. This is true of all triangles, not just ones with 90deg angles. If it had a 90deg angle, this would be a lot easier...

Answer 7

Oh, okay, that makes more sense. How can I tell if a triangle has no solutions or only one solution?

Answer 8

Oh okay, @thenateman27 .. Is the law of cosines useful in this?

Answer 9

@sunny9dragon Please post the actual problem and then we will know how to proceed. Thanks.

Answer 10

The given measurements may or may not determine a triangle. C=37 degrees, a=18, c=9

Answer 11

And I'm supposed to decide whether it is a triangle, an ambiguous case, or not a triangle.

Answer 12

So; sin(37)/9 = sin(A)/18
cross multiply, and simple algebra will give you angle A.

Answer 13

If you're results make sense, then it should work out, but that result makes no sense.

Answer 14

I have a question about another triangle. In the triangle that I will attach shortly after sending this, is it true that this triangle cannot be solved with the law of sines?

Answer 15

That triangle is impossible, yes.