How Far Should You Stand from the Statue of Liberty for the Best Viewing Angle?

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SUMMARY

The optimal distance for a 2-meter tall person to stand from the Statue of Liberty, which is 46 meters tall and sits on a 47-meter plinth, is determined through trigonometric principles. The discussion emphasizes using the Law of Sines and the Law of Cosines to calculate the largest viewing angle. It is suggested that the viewer should experiment with various distances, such as 30m, 40m, 50m, and 66m, to observe the trend in viewing angles. The hint to model the statue and plinth as a straight line simplifies the calculations for determining the best viewing position.

PREREQUISITES
  • Understanding of basic trigonometry, including the Law of Sines and Law of Cosines
  • Ability to model geometric figures, specifically triangles
  • Familiarity with angle measurement and optimization techniques
  • Basic knowledge of the dimensions of the Statue of Liberty and its plinth
NEXT STEPS
  • Learn how to apply the Law of Sines in practical problems
  • Study the Law of Cosines for non-right triangles
  • Explore geometric modeling techniques for optimizing viewing angles
  • Investigate the effects of distance on angle perception in visual studies
USEFUL FOR

Students studying trigonometry, geometry enthusiasts, and anyone interested in optimizing viewing angles in architectural contexts.

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Homework Statement


The statue of libery is 46 meters tall and stands on a plinth 47 meters tall.
How far back should a 2m tall person stand back to obtain the largest viewing angle? There is 66m of land in front of the statue, will the position be within these 66 meters?
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Homework Equations


Law of Sines: sina/A=sinb/B
Law of cosines: b^2=a^2+c^2-2ac(cosB)

The Attempt at a Solution



I just don't understand what the largest viewing angle will be, wouldn't it just be the closest thing to 180 degrees? Also, wouldn't one theoretically be able to view all of the statue from any distance away?
 
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Easiest way might be to try an answer for few values of distance.
hint - assume the statue and plinth are a straight line.

So if you are 1m from plinth you have a narrow angle between a triangle of base 46m starting 45 away
Then try at 66m and then 30m, 40m, 50m and see what the trend is.

hint, if you haven't done much trig you might want to make it a right angle triangle and then find 'A' by working out the total angle and the angle just below A
 

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