We can solve this problem using trigonometry. Specifically, the tangent function is suitable since we are dealing with a right triangle formed by the building, the ground, and the observer’s line of sight to the top of the building.

The tangent function is given by:
$\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}$ Where:

• $\theta = 46.333^\circ$ (angle of elevation)
• Opposite side = 25 m (the height of the building)
• Adjacent side = the distance to the building (let's call it $d$)

Step-by-Step Solution

$\tan(46.333^\circ) = \frac{25}{d}$

Rearranging for $d$:

$d = \frac{25}{\tan(46.333^\circ)}$

Using a calculator:

$\tan(46.333^\circ) \approx 1.043$

$d = \frac{25}{1.043} \approx 23.97 \, \text{m}$

Final Answer

The distance to the building is approximately 23.97 meters.

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Do you want more details or have any further questions?

Here are five related questions to explore:

1. How would the answer change if the building height were 30 m?
2. What is the horizontal distance if the observer is standing on a 5 m platform?
3. What if the angle of elevation is reduced to 30°? How does the distance change?
4. How would you calculate the angle of elevation if the distance is known?
5. How can sine and cosine functions help in different elevation scenarios?

Tip: Always ensure your calculator is in degree mode when working with angles in degrees.