Raymond B. answered • 01/11/22
Math, microeconomics or criminal justice
a = 235, b = 302, alpha = 136.4
alpha is an angle opposite b, which is the largest side of the triangle, since alpha is the largest angle.
in a triangle whose angles sum to 180, 136.4 would have to be the largest angle. And if one of the sides is opposite 136.4, it's the largest side = 302 = b
Let alpha = B, then A = angle opposite a, and C = the angle opposite side c.
A+B+C = 180.
use the law of sines
sinA/a = sinB/b
sinA/235 = sin136.4/302
sinA = 0.5405
A =32.721 degrees
C= 108 - 136.4 - 32.7 = 10.9 degrees
use the law of sines again to get
c = 57
it's a triangle with sides 302, 235, 57 and opposite angles 136.4, 32.7, 10.9 degrees
That's it. Just one triangle
UNLESS alpha could be opposite the other side, the 3rd side not given a length, yet. The question seems to preclude that, but maybe it didn't intend to preclude it.
then do law of sines, cosines and you come up with that 3rd side = 499.2, with the other two angles 18.9 and 24.7 degrees
2 possible triangles
Robert K.
It is not unusual to give a triangle which has no solution. And sometimes there will be the ambiguous case where there are 2 solutions. Misprints do occur, I agree, but my feeling is that this one is not. (btw, I always advise students that even if they feel strongly that there is a misprint to just go ahead and work with what is there and then argue with the teacher about it later!)01/12/22
Robert K.
You and I may disagree about what is a trick question. I feel it is not because the student needs to recognize when no such triangle exists. Most any textbook (yes, I know they are not using textbooks very much these days, unfortunately) will explain this in the chapter and give an example and then in the problem set have 1 or 2 which are like that. Same thing in a test given by the teacher. The student should recognize fairly quickly that this particular problem has no solution and not waste time trying to solve it when he/she could be working on another problem.01/13/22
Robert K.
It is common practice, however, for alpha to be the angle opposite side a. Beta would be the angle opposite side b and gamma would be the side opposite side c. (And alternative practice is to have the angles named as A, B, and C opposite sides a, b, and c respectively.)01/11/22