the following mesurements

Question

the following measurements can describe two possible triangles find both possible measurements for angle A

C=55 degrees

a=10

c=16

Answer 1

I can easily solve the Law of Sines as Mark M. suggested.

It gives an answer for angle A of about 30 degrees.

However, the problem asks for 2 solutions and this is where the difficulty lies.

If you draw the sides and angle as described in the problem, the second point required for angle A does not lie in the triangle which contains angle C; it lies in the triangle which is formed by the supplement of angle C.

Answer 2

By Law of Sines

sin 55° / 16 = sin A / 10

Can you solve for A and answer?