We can use the trigonometric identity for the tangent of a difference of angles:
tan(A - B) = (tan A - tan B) / (1 + tan A * tan B)
We are given sin A and cos B, but we need to find the values of tangent for angles A and B. We can use the Pythagorean identity to find the value of tan A and tan B:
tan^2 A = sin^2 A / cos^2 A = (20/29)^2 / (9/29)^2 = 400/81
tan A = ± 20/9
We choose the positive value of tan A since angle A is in Quadrant 1.
Similarly, we find the value of tan B:
tan^2 B = sin^2 B / cos^2 B = (1 - cos^2 B) / cos^2 B = (1 - (28/53)^2) / (28/53)^2 = 725/729
tan B = ±sqrt(725) / 27
We choose the positive value of tan B since angle B is in Quadrant 1.
Substituting the values of tan A and tan B into the formula for tan(A - B):
tan(A - B) = (20/9 - sqrt(725)/27) / (1 + (20/9)*(sqrt(725)/27))
≈ -0.350
Therefore, the value of tan(A - B) is approximately -0.350.