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

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