Final answer:
By using the tangent function of the angle of elevation, and accounting for Lindsay's eye level, the height of the flagpole is calculated to be approximately 22.9 feet tall, indicating that the flagpole is within the town's height restrictions.
Step-by-step explanation:
To determine whether her school's flagpole is in compliance with Belmont's height restrictions, Lindsay can use trigonometry. The angle of elevation to the top of the flagpole is given as 25 degrees, and she stands 36 feet away from the flagpole. Considering Lindsay's eye level is 5.5 feet, we need to account for this when calculating the height of the flagpole.
We can use the tangent function, which is the ratio of the opposite side to the adjacent side in a right-angled triangle:
- Tan(25 degrees) = Opposite/Adjacent
Given that the adjacent side is the distance from Lindsay to the flagpole (36 feet), the opposite side will be the height of the flagpole above Lindsay's eye level. From the tangent function, we calculate:
- Opposite = Tan(25 degrees) * Adjacent
- Opposite = Tan(25 degrees) * 36 feet
After finding the opposite side, we add Lindsay's eye level to determine the total height of the flagpole:
- Total height of flagpole = Opposite + Lindsay's eye level
To solve for the opposite side:
- Opposite = Tan(25 degrees) * 36 feet ≈ 17.4 feet
To find the total height of the flagpole:
- Total height of flagpole = 17.4 feet + 5.5 feet ≈ 22.9 feet
Therefore, Lindsay's school flagpole, to the nearest tenth of a foot, is approximately 22.9 feet tall and in compliance with the town's regulations.