The two triangles in the image are similar (i.e., their corresponding angles are equal, and their corresponding sides are proportional). To find the scale factor from Figure $A$ to Figure $B$, we compare the lengths of corresponding sides.

From the image:

• The corresponding sides of Figure $A$ and Figure $B$ are $15$ and $5$ respectively.

The scale factor can be calculated as: $\text{Scale factor} = \frac{\text{Side length of Figure A}}{\text{Side length of Figure B}} = \frac{15}{5} = 3$

Thus, the scale factor from Figure $A$ to Figure $B$ is 3.

Do you want more details or have any questions? Here are five related questions you might explore:

1. What would the scale factor be if the transformation was from Figure $B$ to Figure $A$?
2. How do you verify that two triangles are similar?
3. What effect does scaling have on the area of a figure?
4. Can you find the ratio of the perimeters of Figure $A$ and Figure $B$?
5. How does the concept of scale factor apply in real-world applications like maps or models?

Tip: When two shapes are similar, their corresponding angles are congruent, and the ratios of their corresponding sides are equal!