To find the actual height of the building, we use the proportion between the dimensions of the scale model and the actual building.

Given:

• Scale model width: $7 \, \text{inches}$
• Scale model height: $15 \, \text{inches}$
• Actual building width: $420 \, \text{feet}$
• Actual building height: $h \, \text{feet}$ (to be determined)

We set up the proportion:

$\frac{\text{Scale Model Width}}{\text{Actual Width}} = \frac{\text{Scale Model Height}}{\text{Actual Height}}$

Substituting the values:

$\frac{7}{420} = \frac{15}{h}$

Step 1: Solve for $h$

Cross-multiply:

$7h = 420 \times 15$

$7h = 6300$

Divide both sides by 7:

$h = \frac{6300}{7} = 900$

Final Answer:

The actual height of the building is 900 feet.

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Would you like further clarification or details about proportions?

Here are some related questions to consider:

1. What is a proportion, and how is it used in scaling?
2. How do we determine scale factors in models and maps?
3. Can you explain why cross-multiplication works in solving proportions?
4. How would the solution change if the scale model had different dimensions?
5. How is this concept applied in architecture or engineering?

Tip: Always double-check units in your calculations to ensure consistency, especially when converting between different measurement systems.