To solve this problem, we can use trigonometry. The scenario describes a right triangle, where the angle of elevation is 23.7°, the adjacent side (distance from the point of observation to the tower) is 5280 feet, and the opposite side is the height of the tower. We're asked to find the height of the tower.

We will use the tangent function from trigonometry, which is defined as:

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

Given:

• $\theta = 23.7^\circ$
• Adjacent = 5280 feet
• Opposite = height of the tower (which we need to find)

Rearrange the equation to solve for the height (opposite):

$\text{height} = \tan(23.7^\circ) \times 5280$

Let's calculate the height.

math

Given values

theta_deg = 23.7 # Angle in degrees adjacent = 5280 # Distance from the tower in feet

Convert angle to radians

theta_rad = math.radians(theta_deg)

Calculate the height of the tower

height = math.tan(theta_rad) * adjacent height_rounded = round(height) # Round to the nearest foot

height_roundedThe height of the tower is approximately 2318 feet, rounded to the nearest foot.

Would you like further details or have any additional questions? Here are some related questions to explore:

1. How do we use other trigonometric functions (e.g., sine or cosine) in similar problems?
2. What happens if the angle of elevation changes to a different value?
3. How would you solve this problem if the distance from the tower was different?
4. What is the role of converting angles to radians when using trigonometric functions?
5. How do you solve a right triangle if you're given the height and the angle of elevation?

Tip: When solving problems involving angles of elevation or depression, always remember to check if you need to convert angles to radians before using trigonometric functions!