We can solve this problem using trigonometry, specifically the tangent function, since we have an angle and the opposite and adjacent sides of a right triangle.

Given:

• Angle of elevation = $5^\circ$
• Distance from the base of the building = $1$ mile = $5280$ feet
• Height of the building = $h$ (to be found)

Using the tangent function: $\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}$ $\tan(5^\circ) = \frac{h}{5280}$

Now, solving for $h$:

$h = 5280 \times \tan(5^\circ)$

Let's calculate: math

Given values

theta = 5 # degrees distance = 5280 # feet

Calculate height using tangent function

height = distance * math.tan(math.radians(theta)) round(height, 2)The height of the building is 461.94 feet when rounded to two decimal places.

Would you like a step-by-step breakdown of the calculations?

Here are 5 related questions to explore further:

1. What would be the height if the angle of elevation were 10 degrees