Final answer:
To find sin b in triangle ABC, use the equation sin b = sin (180° - A - C), where A, B, and C are the angles of the triangle. Given that sin A = 2/3, solve for angle A using the inverse sine function: A = sin^-1(2/3). Then, find angle C by subtracting A and B from 180°: C = 180° - A - B. Finally, find sin b using sin b = sin C.
Step-by-step explanation:
To find sin b in triangle ABC, we can use the equation sin b = sin (180° - A - C), where A, B, and C are the angles of the triangle. Given that sin A = 2/3, we can solve for angle A using the inverse sine function: A = sin-1(2/3). Then, we can find angle C by subtracting A and B from 180°: C = 180° - A - B. Finally, we can find sin b using sin b = sin C.
Step 1: Find angle A using A = sin-1(2/3).
Step 2: Find angle C using C = 180° - A - B.
Step 3: Find sin b using sin b = sin C.