To find the length of $\overline{AB}$, let's analyze the information provided in the image:

• The angle $\angle ABC = 61^\circ$.
• The angle $\angle BAC = 47^\circ$.

Given that these are angles in a triangle, the third angle $\angle ACB$ can be calculated using the fact that the sum of the angles in a triangle is $180^\circ$:

$\angle ACB = 180^\circ - 61^\circ - 47^\circ = 72^\circ$

To find the length $\overline{AB}$, we can use the Law of Sines, which states:

$\frac{AB}{\sin(\angle ACB)} = \frac{BC}{\sin(\angle BAC)} = \frac{CA}{\sin(\angle ABC)}$

Since the specific lengths are not given directly, we can't apply the Law of Sines directly. However, given the multiple-choice options and the typical structure of such problems, it's reasonable to assume that the length $\overline{BC}$ is available or assumed in such problems.

Let’s assume $\overline{BC}$ is the length of 53.74 units (as the options provided can sometimes hint at this).

Now, using the Law of Sines:

$\frac{AB}{\sin(72^\circ)} = \frac{53.74}{\sin(47^\circ)}$

Solving for $AB$:

$AB = \frac{53.74 \times \sin(72^\circ)}{\sin(47^\circ)}$

Let's calculate this expression.

The calculated length of $\overline{AB}$ is approximately $69.88$ units. This value does not match any of the provided multiple-choice options.

Since this could mean either the assumed value of $\overline{BC}$ is incorrect or additional context is missing, let's reconsider the options. It seems we should correct the calculation by adjusting the assumption or perhaps use a different side length as the correct one.

Would you like to attempt using different side lengths or provide additional information to better refine the solution?

Here are some relative questions:

1. Should we try another side length to see if it matches the options?
2. Could there be a typographical error in the options provided?
3. Are we sure the $\overline{BC}$ length was meant to be assumed?
4. What if the problem provided more specific side lengths?
5. Can the image's context suggest a different interpretation?
6. Should we consider possible approximations in the multiple-choice options?
7. Could there be additional information outside the image that may assist in solving this?
8. Is there any reference material that could clarify the problem's structure?

Tip: Always double-check the provided problem's conditions, especially when dealing with multiple-choice answers.