can you help me find a side length or even an angle on a triangle with only two side lengths and no angles. also its not a right triangle

Question

one side length is 90 and the other is 368 and i know that the missing one is greater than 458

Answer 1

4 unknowns = 3 missing angles + 1 missing sides

law of cosines:

C^2 = A^2 + B^2 - 2 A B cos c

C^2 = 90^2 + 368^2 - 2(90)(368) cos c

C^2 = 143524 - 66240 cos c <--- 1st equation

sin c / C = sin b/ 368 = sin a / 90

2 equations from this

it is SUPPOSED to be a 4 x 4 non-linear system,

but it is not because of the equations...

C^2 = 143524 - 66240 cos c

sin c/C = sin b/368

sin c/C = sin a/90

sin b / 368 = sin a / 90

THe 2nd and 3rd are the same as the last

Another equation is needed

Answer 2

No, it's not solvable. The triangle isn't uniquely defined as you can vary the angle between the two given sides. You need the third side (to solve for angle(s)) or the included angle to find the third side (then you can use the cosine law to solve for angles).

Answer 3

the sum of 2 sides of a triangle cannot be larger than the 3rd side

90+368 = 458

This is not a triangle, or at best a degenerate triangle that collapsed into a line with

angles 0,0 and 180 and sides 90, 368 and exactly 458

angle opposite 458 is 180 degrees or pi radians

angles opposite each other side is zero degrees or zero radians

area of the "triangle" = zero

perimeter = 916