Calculating Building Height Using Trigonometry | Surveyor's Method

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SUMMARY

The discussion focuses on calculating the height of a building using trigonometric principles, specifically the tangent function. A surveyor measures angles of pi/3 and pi/4 from different distances, leading to the conclusion that the building's height is approximately 94.6 feet. The calculations involve using the tangent of the angles to establish relationships between the height and distances from the building. The second part of the problem explores the angle from a further distance of 20 feet, resulting in an angle of approximately 39.5 degrees.

PREREQUISITES
  • Understanding of basic trigonometry, specifically tangent functions.
  • Familiarity with angle measurements in radians.
  • Knowledge of solving equations involving distances and heights.
  • Ability to apply the surveyor's method in practical scenarios.
NEXT STEPS
  • Study the properties of tangent functions in trigonometry.
  • Learn how to apply the Law of Sines and Cosines in surveying.
  • Explore advanced trigonometric applications in real-world surveying tasks.
  • Investigate the use of surveying tools and software for height calculations.
USEFUL FOR

This discussion is beneficial for surveyors, civil engineers, and students studying trigonometry or surveying techniques, particularly those interested in practical applications of trigonometric calculations in determining heights and distances.

anthonym44
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A surveyor stands on flat ground at an unknown distance from a tall building. She measures the angle from the horizonal ground to the top of the building; this angle is pi/3. next she paces 40ft further away from the building. the angle from the ground to the top of the building is now measured to be pi/4.
a)how tall is the building
b) If the surveyor moves 20 feet further from the building what will the angle from the horizontal to the building's roof be.








The Attempt at a Solution


i think i got this one right, but I am new to the site so i thought i would just check myself with this problem. i got equation 40 + x = y beause the horizontal axis must equal the vertical when the angle is 45 degrees (pi/4). Then i used tan(60) = y/x to solve for x and then i subsituted eventually solving for y. my final answer is 94.8ft. part B asks for the angle if the person moves further back 20 ft. i just added that length to 94.8 and used tan to solve eventually getting the angle to be 39.5 degrees. If anyone has the time can they check the work to make sure i did it correctly? Thanks.
 
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Yup, that's right. I get something closer to 94.6 ft for the height though.
 
thanks for your help Dick.
 

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