Final answer:
The height of the flagpole is found using the tangent function of trigonometry, calculating the height from eye level to the top of the pole, and then adding the person's eye level above ground. The flagpole's height is 32ft to the nearest whole foot.
Step-by-step explanation:
To find the height of the flagpole, we can use trigonometry, specifically the tangent function which relates angles to opposite and adjacent sides in a right-angled triangle. The angle of elevation to the top of the flagpole is given as 35°, and the horizontal distance from the person to the base of the flagpole is 40ft. The person's eye level is 4ft above the ground, which will need to be added to the calculated height from eye level to the top of the pole.
We can express this relationship as:
tangent(35°) = opposite / adjacent
Therefore,
height from eye level to top of pole = tangent(35°) × 40ft
height of flagpole = height from eye level to top of pole + 4ft (eye level)
Let's calculate:
height from eye level to top of pole = tangent(35°) × 40ft
= 0.7002 × 40ft
= 28.008ft
Rounding to the nearest whole foot, we get 28ft as the height from eye level to the top of the pole.
Therefore, the height of the flagpole is:
height of flagpole = 28ft + 4ft
= 32ft
To the nearest whole foot, the height of the flagpole is 32ft.