In ABC, sin A=88, sin B=42, and a =17, find the length of b.

I believe there is a mistake in your question as the sine of an angle in a triangle cannot be greater than 1. The sine function represents the ratio of the length of the opposite side to the hypotenuse in a right-angled triangle, and thus it's always a value between -1 and 1. However, if we assume that you meant sin A = 0.88 and sin B = 0.42, we could approach the problem.

To find the length of side b in triangle ABC using the sine rule, which states that the ratio of the length of a side of a triangular to the sine of the opposite angle is the same for all three sides of the triangle. The Law of Sines is expressed as:

a/sin A = b/sin B = c/sin C

In this problem, we are given side a (which is 17) and the sine of angles A (which is assumed to be 0.88) and B (which is 0.42). We want to find the length of side b. We rearrange the Law of Sines to solve for b:

b = a * (sin B / sin A)

Plugging in the known values:

b = 17 * (0.42 / 0.88) b = 17 * 0.47727272727272... b ≈ 17 * 0.4773 b ≈ 8.1141

The length of side b is approximately 8.1141 units.