The length of side b is approximately 8.8 inches.
The law of sines asserts that in any triangle ABC: In order to find the length of side b in any triangle ABC:
A/Sin = B/Sin + C/Sin
where the side lengths are a, b, and c and the angles are a, b, and c.
We are informed of the following:
9.3 inches, so a
B = 75°\sC = 17°
We can apply the ratio to determine the length of b:
b/sin B equals a/sin A
After solving for b and substituting in the provided values, we obtain:
75° b/sin = 9.3° sin A
b = (9.3*sin75°) / sinA
We can use the fact that a triangle's angles sum to 180° to determine sin A:
A + B + C = 180°
A + 75° + 17° = 180°
A = 88°
If we replace with sin 88° and sin 75°, we obtain:
B is equal to (9.3 * sin 75°)/sin 88°.
b=8.8 inches (rounded to the nearest 10th of an inch)
As a result, side B measures around 8.8 inches long.