trig question: does these measurements determine 1 or 2 triangles?

Question

I'm supposed to state whether the given measurements determine zero, one, or two triangles. (It's an SSA [some like to reverse it]triangle)

C=30 degrees
a=32
c=16

I got one but I'm not completely sure because when I did the problem I got A = 90 degrees and techncally if you subtract 180 from 90 you get 90 and then add the 30 degrees from the given you only get 120 which is less than 180 meaning it should determine 2 triangles but the only problem with that is that you get 2 90 degree angles in a triangle... So because of that I think it's one.

If someone could solve it and tell me what they get and why?

so does the measurements determine one triangle as I think or is it 2? I know it is definitely not zero.

Answer 1

By the law of sines, sure enough angle A must be 90 degrees. That makes side a the hypotenuse of a 30-60-90 triangle. There is only one triangle. The third side is 16sqrt(3), and the third angle 60 degrees.

Answer 2

I have to assume the 30 degrees is the only angle. What you have is an obtuse triangle 32?high and 16?wide with a 30 degree angle on one side where the 2 lines join.Triangles do not necessarily have 90 degree angles, unless you are dealing only with right triangles Pythagerooney rules!

Answer 3

Use a appropriate triangle with hypotenuse 12 feet, one leg x feet and yet another leg 8 feet. enable x = the gap between the backside of the tent and the stake. We use a^2 + b^2 = c^2 to discover x. 8^2 + x^2 = 12^2 sixty 4 + x^2 = one hundred forty four x^2 = one hundred forty four - sixty 4 x^2 = eighty We take the sq. root of the two factors. x = 4(sqrt{5}) feet the gap from the backside of the tent to the stake is 4(sqrt{5}) feet, that's close to 9 feet. to discover the attitude, we use a trig function. yet, which trig function? we can use the sine, cosine or tangent function because of the fact all of us comprehend the two legs and the hypotenuse of the marvelous triangle. i'll apply sine. enable A = attitude sin(A) = 8/12 i might desire to apply the sine inverse key because of the fact i'm searching for an attitude. A = sin^-a million(8/12) A = 40-one.eighty one stages

Answer 4

Yes it is true. You just get one right triangle.

Answer 5

one triangle