Final Answer:
The value of x in the given problem is approximately x ≈ 37 degrees when rounded to the nearest degree.
Step-by-step explanation:
In the previous problem, we found that the solution to the trigonometric equation cos(x + b)sin x = 15/17 with sin b = 4/5 is x = arcsin(4/5) in quadrant I and x = π - arcsin(4/5) in quadrant II. To find the value of x, we can use a calculator to evaluate these expressions.
For quadrant I: x = arcsin(4/5) ≈ 37 degrees.
For quadrant II: x = π - arcsin(4/5) ≈ 143 degrees.
Since we are asked to round to the nearest degree, the value of x is approximately x ≈ 37 degrees.
This rounding is done because angles are often measured in degrees, and rounding to the nearest degree provides a practical and meaningful representation of the angle in many real-world applications.