Possible? (1 Viewer)

[Trebla]

Hi there,

Is it possible to form this triangle XYZ?

XY = 12
YZ = 8
angle ZXY = 68 degrees
angle YZX = 72 degrees
angle XYZ = 40 degrees

Reason I asked is because I encountered this trig question and when I applied the cosine rule to find XZ, I get a different answer for XZ to when I apply the sine rule to find XZ.

I also found that the sine rule is not satisfied using the two known sides (12/sin 72 =/= 8/sin 68). I've also tried physically constructing the triangle and I couldn't do it, so I concluded that this triangle doesn't exist.

Is there something wrong with my working or does it really not exist?
If it doesn't exist why is that so? The triangle inequality seems to be satisfied but is there some condition on the angles I'm not aware about?

I'm gonna feel like an idiot if it turns out my working is wrong....lol

 

[Iruka]

I think the problem is that the triangle is *almost* isosceles, if you look at the size of the angles, but actually nothing like isosceles if you look at the lengths of the sides you have been given, which is why the sine rule is not working.

 

[SpinCobra]

The easiest way is probably to draw the triangle out.

The smaller the angle, the side on the opposite has to be smaller.

Since 40 degrees corresponds to side of 12. Whereas the angle 68 degrees corresponds to a side of 8.

This means that the triangle is screwed/doesnt work.