To find the height of the actual building based on the scale model, you need to multiply the height of the model by the scale ratio.

The given scale is $1 \text{ inch} : 75 \text{ feet}$, meaning for every 1 inch of the model, the actual building is 75 feet tall.

The height of the model is given as $19 \frac{2}{5} \text{ inches}$.

Step-by-step solution:

1. Convert the mixed number $19 \frac{2}{5}$ into an improper fraction: $19 \frac{2}{5} = \frac{19 \times 5 + 2}{5} = \frac{95 + 2}{5} = \frac{97}{5}$

2. Now, multiply the height of the model by the scale ratio: $\text{Height of actual building} = \frac{97}{5} \times 75$

3. Simplify the multiplication: $\frac{97}{5} \times 75 = \frac{97 \times 75}{5} = \frac{7275}{5} = 1455 \text{ feet}$

So, the actual height of the building is 1455 feet.

Would you like any additional details or clarifications?

Here are some related questions:

1. What would be the height of the model if the actual building were 1200 feet tall?
2. If the scale were changed to 1 inch: 100 feet, what would the new model height be for the same building?
3. How do you calculate the actual dimensions of a building when given a model's length and width?
4. If another model uses a scale of 1 inch: 50 feet, how would this affect the model's height compared to the original?
5. How can we convert between different scale units, such as meters instead of feet?

Tip: Always ensure that the scale units match when making comparisons between model dimensions and actual dimensions.