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 determine the horizontal distance between the bases of skyscraper \( A \) and skyscraper \( B \), we can use trigonometry, specifically the tangent function which relates angles to opposite and adjacent sides in right triangles. **Given:** - Height of skyscraper \( B \) (\( h \)) = 1,471 feet - Angle of inclination (\( \theta \)) = \( 10.1^\circ \) **Objective:** Find the horizontal distance (\( d \)) between the two skyscrapers. **Approach:** 1. **Understanding the Scenario:** - Imagine a right triangle where: - The opposite side is the height of skyscraper \( B \) (\( 1,471 \) feet). - The angle of inclination from the base of \( A \) to the top of \( B \) is \( 10.1^\circ \). - The adjacent side is the horizontal distance (\( d \)) we need to find. 2. **Using the Tangent Function:** - The tangent of an angle in a right triangle is the ratio of the opposite side to the adjacent side: \[ \tan(\theta) = \frac{\text{Opposite}}{\text{Adjacent}} = \frac{h}{d} \] - Rearranging to solve for \( d \): \[ d = \frac{h}{\tan(\theta)} \] 3. **Calculating the Tangent:** - First, find \( \tan(10.1^\circ) \). - Using a calculator: \[ \tan(10.1^\circ) \approx 0.1781 \] 4. **Calculating the Distance \( d \):** - Plug in the values: \[ d = \frac{1,471 \text{ feet}}{0.1781} \approx 8,250 \text{ feet} \] **Conclusion:** The horizontal distance between skyscraper \( A \) and skyscraper \( B \) is approximately **8,250 feet**. **Final Answer:** The two skyscrapers are approximately 8 250 feet apart.