Trigonometry: Another Statics Problem

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SUMMARY

The discussion centers on a trigonometry problem involving a surveying error in a subdivision lot measuring 200 ft by 80 ft. The surveying crew's error of 0.10 degrees leads to a misplacement of the iron pin. Using the tangent function, the user calculates the distance the pin is off from the true corner to be approximately 0.349 feet, confirming the accuracy of their solution.

PREREQUISITES
  • Understanding of basic trigonometric functions, specifically tangent.
  • Familiarity with right triangle properties.
  • Knowledge of angle measurement in degrees.
  • Ability to perform basic calculations involving feet and angles.
NEXT STEPS
  • Study the application of the tangent function in real-world surveying problems.
  • Learn about error analysis in surveying and its implications.
  • Explore advanced trigonometric concepts such as sine and cosine for more complex problems.
  • Investigate the use of surveying tools and techniques for accurate measurements.
USEFUL FOR

Students in mathematics or engineering fields, surveying professionals, and anyone interested in applying trigonometry to real-world problems.

blixel
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Homework Statement


A subdivision lot is 200 ft long by 80 ft wide. A surveying crew made an error of 0.10 degrees when setting the iron pin in the corner of the lot shown. By what distance is the correct pin off of the true corner?

Problem%2014_zpsjucnp3ue.png


Homework Equations


I think I'm doing this one right also, but it's an even numbered problem so I can't check my answer.

The Attempt at a Solution


I'm treating the left part of the image as a right triangle. I'm saying that theta=0.10 degrees, and theta is located at the top of the triangle. So the opposite is the short piece at the bottom, and that's what I'm trying to find.

tan(theta)=opposite/adjacent

Adjacent is along the side, and it's 200 feet.

opposite=200*tan(0.10)~=0.349 feet.

So, if I've done this right, the distance is off by 0.349 feet.
 

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That's what I get, as well.
 
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