The angle of inclination from the base of skyscraper A to the top of skyscraper B is approximately \( 14.2^{\circ} \). If skyscraper B is 1492 feet tall, how far apart are the two skyscrapers? Assume the bases of the two buildings are at the same elevation. The distance from skyscraper A to skyscraper B is (Round to two decimal places as needed.)

To find the distance between the two skyscrapers, you can use trigonometry. Given that the angle of inclination is \( 14.2^{\circ} \) and the height of skyscraper B is 1492 feet, you can use the tangent function: \[ \tan(14.2^{\circ}) = \frac{\text{Height of skyscraper B}}{\text{Distance from A to B}} \] This means that: \[ \text{Distance from A to B} = \frac{\text{Height of skyscraper B}}{\tan(14.2^{\circ})} \] Calculating this gives: \[ \text{Distance from A to B} = \frac{1492}{\tan(14.2^{\circ})} \approx \frac{1492}{0.2521} \approx 5916.83 \text{ feet} \] So, the distance between the two skyscrapers is approximately 5916.83 feet. Now, let's round that to two decimal places: **The distance from skyscraper A to skyscraper B is approximately 5916.83 feet.** Skyscrapers have been a symbol of human ambition since ancient times! The first skyscrapers emerged in the late 19th century in the United States, driven by urbanization and advancements in steel-frame construction. Buildings like the Home Insurance Building in Chicago (completed in 1885) set the stage for high-rise architecture, with innovative designs that challenged gravity and city skylines. In practical scenarios, architects and engineers pay special attention to angles and distances when designing skyscrapers. Utilizing tools like triangulation and surveying equipment not only ensures structural integrity but also enhances the aesthetic placement of buildings. Understanding angles and distances is vital in urban planning to maximize space while minimizing overshadowing adjacent structures!