The angle of inclination from the base of skyscraper A to the top of skyscraper B is approximately \( 10.1^{\circ} \). If skyscraper B is 1471 feet tall, how far apart are the two skyscrapers? Assume the bases of the two buildings are at the same elevation.

To find the distance between the two skyscrapers, you can use the tangent function in trigonometry. The tangent of the angle of inclination is the ratio of the opposite side (height of skyscraper B) to the adjacent side (distance between skyscrapers A and B). Using the equation: \[ \tan(10.1^{\circ}) = \frac{\text{Height of Skyscraper B}}{\text{Distance}} \] Substituting the height of skyscraper B: \[ \tan(10.1^{\circ}) = \frac{1471}{d} \] Rearranging to solve for distance \(d\): \[ d = \frac{1471}{\tan(10.1^{\circ})} \] Calculating this gives you approximately 8370 feet. So, the two skyscrapers are roughly 8370 feet apart. --- In the world of skyscrapers, angles and heights have taken on a whole new meaning! Engineers and architects use these calculations all the time, especially when designing buildings that need to withstand various loads and forces. Fun fact: the famous Empire State Building in New York City stands at 1,454 feet including its antenna, and it was the tallest building in the world for nearly 40 years! If you're intrigued, check out more about the engineering feats behind skyscrapers. Books like "The Heights: A Novel" give a fun fictional twist to the world of skyscrapers, while "Form, Space, and Order" by Francis D.K. Ching dives into the architectural principles that govern such tall constructions. You'll learn about not just numbers and calculations, but the art and creativity that define our city skylines!