a person is standing 40ft from a flagpole and can see the top of the pole at a 35 degree angle of elevation. the persons eye level is 4ft from the grond. what is the height of the flagpole to the nearest foot
To find the height of the flagpole, we can use trigonometry.
Let's name the height of the flagpole as 'h'.
We have a right triangle formed by the person, the top of the flagpole, and the base of the triangle (the distance between the person and the flagpole), which is 40ft.
We know that the person's eye level is 4ft from the ground. This creates another right triangle, which has a height of 4ft from the ground to the person's eyes, and the base is also 40ft.
Because the person can see the top of the flagpole at a 35-degree angle of elevation, we can use the tangent function to find the height of the flagpole.
The tangent of an angle is the ratio of the opposite side to the adjacent side.
In this case, the opposite side is the height of the flagpole (h), and the adjacent side is the distance between the person and the flagpole (40ft).
So, we have:
tan(35°) = h / 40ft
To solve for h, we rearrange the equation:
h = 40ft * tan(35°)
Calculating this using a calculator, we get:
h ≈ 40ft * 0.7002
h ≈ 28.008ft
So, the height of the flagpole to the nearest foot is 28ft.