Question

Explain why using the law of sines when given SSA information can result in one, two, or no triangles.

Answer 1

Due to the ambiguous case of the law of sines, two different triangles could be created. There may be a second angle if you are given two sides and the angle not in between. The ambiguous case may result in one solution, two solutions or no solutions therefore there can be one, two or no triangles.

Answer 2

Explanation:

Whenever SSA information is given, we have

a/sinA = b/sin B = c/sin C

When we know a and sin A, and b we can solve for sin B.

When sin B is known, we can have B take two values one in the I quadrant less than 90 and one in the ii quadrant more than 90.

Sometimes both angles have to be taken as solutions for two triangles.

In these cases, we can get two triangles as solution for the given information.

For example, if A =20 degrees and if we get sinB=1/2 then we can have B as either 30 or 150 since both consistent when added with 20 gives less than 180

In these cases we get two triangles as solution.

If A = 40 say then we can have B only taking 30.

In this case one solution.

No triangle is possible only when sum of two sides exceed third side in other words the given information do not form a triangle.