Question

A person stands 35.0 m from a flag pole. With a protractor at eye level, he finds that the angle to the top of the flag pole is 25.0 degrees. How high is the flag pole?

Answer 1

To find the height of the flag pole, one can use the tangent function from trigonometry, where the tangent of the angle of elevation equals the ratio of the height of the flagpole to the distance from the observer to the pole. After substituting the known values and calculating, the height of the pole can be determined.

Step-by-step explanation:

The question asks how high the flag pole is, given that a person stands 35.0 m away from it and observes the top of the pole at an angle of 25.0 degrees above the horizontal. To solve for the height of the flag pole, we can use trigonometry, specifically the tangent function, which relates the angle of elevation to the opposite side and adjacent side of a right triangle.

The formula we would use is:

tangent(angle) = opposite/adjacent

Here, the opposite side is the height of the flag pole (which we want to find), and the adjacent side is the distance from the person to the flag pole (35.0 m).

tan(25.0 degrees) = height / 35.0 m

After calculating, we would find the height of the flag pole.

Answer 2

The flag is 16.321 meters high.

Step-by-step explanation:

The situation is represented in the attached figure

In the figure we have

`tan(\theta )=(H)/(D)`

Given that

θ = 25.0 degrees

D = 35.0 meters

Applying values in the above equation we have

`tan(25)=(H)/(35.0)\\\\\therefore H=35.0* tan(25^(o))=16.321meters`