posted by Jon on .
In triangle ABC, A=35 degrees, a=43, and c=20. Determine whether ABC has no solution, one solution, or two solutions. Then solve the triangle. Round to the nearest tenth.
According to the law of sines,
sin C = c* sin A/a = 0.2668
C = 15.5 degrees, or 164.5 degrees. Only the 15.5 is possible without exceeding 180 degrees for all angles. That means B = 180 - 35 - 15.5 = 129.5 degrees. There is only one solution in this case, although some side-side-angle specified triangles (like this one) have two solutions.
b = sin B* a/sin A = 57.8
I get the work part of it but for this question is it one solution or two?
What I tried to say is that sometimes when two adjacent sides of a triangle are specified, along with the angle adjacent to one side, two solutions are possible. This called the "ambiguous Side-Side-Angle" case. This is a Side-Side-Angle case, but it turns out that only one solution is possible anyway. One of the two computed angles from the law of sines is too large to make a triangle possible.