We can solve this problem using trigonometry, specifically the tangent function, which relates the angle of elevation to the opposite and adjacent sides in a right triangle.

The tangent of an angle $\theta$ is given by:

$\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}$

In this case:

• The angle of elevation $\theta = 9^\circ$
• The adjacent side is the horizontal distance from the base of the building, which is 1.2 miles.
• The opposite side is the height of the building (which we are trying to find).

First, we need to convert the distance from miles to feet, as the problem asks for the height in feet.

1 mile = 5280 feet, so: $1.2 \text{ miles} = 1.2 \times 5280 = 6336 \text{ feet}$

Now, using the tangent function: $\tan(9^\circ) = \frac{\text{height of the building}}{6336 \text{ feet}}$

Solving for the height of the building: $\text{height of the building} = 6336 \times \tan(9^\circ)$

Using a calculator to find $\tan(9^\circ)$: $\tan(9^\circ) \approx 0.1584$

Now, calculate the height: $\text{height of the building} = 6336 \times 0.1584 \approx 1003.6 \text{ feet}$

Thus, the height of the building is approximately 1003.6 feet.

Would you like more details or have any questions?

Here are 5 related questions to expand on this:

1. How would the height change if the distance were doubled to 2.4 miles?
2. What would the angle of elevation need to be for a building 1500 feet tall at the same 1.2-mile distance?
3. How does the tangent function relate to other trigonometric functions like sine and cosine?
4. How would this calculation change if the building were on a hill, and we accounted for the hill’s slope?
5. What is the importance of angle precision in calculating the height of tall buildings?

Tip: Always convert units to match the final required answer before solving the problem.