Error in the height of a flagpole

So dh = 4dx/3In summary, the question is asking for the error in the calculated height of a flagpole given an observer's distance and angle of elevation, with a possible error of 0.02 radians. Using the tangent line approximation, the solution involves setting up an equation and substituting values to find the error in the calculated height.
  • #1
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Homework Statement


An observer is 6m from the base of a flagpole. The angle of elevation of the top of the pole is measured as pi/3, with a possible error of 0.02 radians. Use the tangent line approximation to find the error in the calculated height of the pole.



Homework Equations


Tangent line approximation.



The Attempt at a Solution


My troubles here seem to be in setting up the proper equation. I started by drawing a right angle triangle, with the formula obtained from it being h=6tanx. I then took the derivative of this and plugged in pi/3 for x. Using pi/3, i then found a value for h, and set up the equation of the line. I then tried to plug 0.02 in for the x value in the line equation, and naturally this got me nowhere. The setup for this question is just stumping me entirely; I know how to use the tangent line approximation, so that is no problem, it's just finding out how to bring the 0.02 value into the solution. If anyone can be of help here I would appreciate it greatly, thanks.
 
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  • #2
h= 6tanx
so dh = 6sec^2x*dx
Substitute the values to get dh
 

1. What is the definition of "Error in the height of a flagpole"?

The error in the height of a flagpole refers to the difference between the actual height of a flagpole and the intended or stated height. It is a measure of how accurately the flagpole's height has been determined or measured.

2. What causes errors in the height of a flagpole?

Errors in the height of a flagpole can be caused by a variety of factors, such as human error in measuring or recording the height, variations in the ground level where the flagpole is installed, or changes in weather conditions that affect the flagpole's height.

3. How is the error in the height of a flagpole calculated?

The error in the height of a flagpole is calculated by taking the difference between the actual height and the intended or stated height of the flagpole. This value is usually expressed in either inches or feet.

4. How can errors in the height of a flagpole be minimized?

To minimize errors in the height of a flagpole, it is important to use precise measuring tools and techniques, ensure that the ground is level where the flagpole is installed, and take into account any potential weather conditions that may affect the flagpole's height.

5. Why is it important to accurately measure the height of a flagpole?

Accurately measuring the height of a flagpole is important for several reasons. It ensures that the flagpole is installed correctly and stands at the intended height. It also ensures that the flag is properly displayed and respects the proper flag etiquette. In addition, accurate measurements are important for construction and engineering purposes, as well as for maintaining safety standards.

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