Question

If the measure of angle A is 40* and the length of side b is 15 inches, which can be the length of side a if it is possible to form two triangles

Answer 1

Because ∠A=40°, therefore ∠B + ∠C = 180.

To create two triangles, we could make a = 10 in.

From the Law of Sines,
a/sinA = b/sinB.
 
Therefore
10/sin(40) = 15/sin(B)
sin(B) = (15/10)*sin(40) = 0.9642
∠B = arcsin(0.9642) = 74.6°

Because the sine function is positive in quadrants 1 and 2, we could also have ∠B = 180 - 74.6 = 105.4°.
This means that
a/sin(105.4) = 15/sin(40°)
a = [sin(105.4)/sin(40)]*15 = 22.5 in

Answer:
We could have a = 10 in, or a = 22.5 in