Using the law of sines with angles A = 32°, side b = 7 in, and angle C = 38°, we find side a ≈ 4.6 inches. Option B is the correct choice.
We can use the law of sines to solve for the missing side length. The law of sines states that the ratio of the sine of an angle in a triangle to the opposite side length is equal to the ratio of the sine of another angle in the triangle to the opposite side length.
In this case, we have:
* Angle A = 32°
* Side b (opposite to angle A) = 7 in
* Angle C = 38°
We want to solve for side a (opposite to angle C).
Using the law of sines, we can write the following equation:
sin(A) / b = sin(C) / a
Substituting the known values, we get:
sin(32°) / 7 in = sin(38°) / a
Solving for a, we get:
a = 7 in * sin(38°) / sin(32°)
≈ 4.6 in
Therefore, the length of side a is approximately 4.6 inches. So, Option B is the correct choice.