Asked by Jon
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.
no solution.
no solution.
Answers
Answered by
drwls
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
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
Answered by
Jon
I get the work part of it but for this question is it one solution or two?
Answered by
drwls
One
Answered by
drwls
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.