Final answer:
To solve for the length b in a right triangle, you should use the trigonometric function tangent (tan) of angle B.
Step-by-step explanation:
To solve for the length b in a right triangle, we can use the trigonometric function tangent (tan) of angle B. So the correct function to use is option a, which is: a times tan(B) = b. This is because the length a is the adjacent side to angle B, and tangent is defined as the ratio of the length of the opposite side to the adjacent side in a right triangle.