Solving Angle of Elevation Problem: 200 ft, 70°, 82°

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SUMMARY

The problem involves calculating the height of a flagpole using trigonometric principles based on given angles of elevation and a fixed distance. The angle of elevation to the base of the flagpole is 70°, and to the top is 82°, with the observer positioned 200 ft away. The solution requires the application of basic trigonometric functions rather than the Law of Sines, focusing on right-angled triangles formed by the observer's line of sight.

PREREQUISITES
  • Understanding of basic trigonometry, specifically right-angled triangles
  • Familiarity with sine and tangent functions
  • Ability to interpret angles of elevation
  • Skill in diagramming geometric problems
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  • Study the properties of right-angled triangles in trigonometry
  • Learn how to apply the tangent function to solve height problems
  • Explore the relationship between angles of elevation and distances in trigonometric contexts
  • Practice solving similar problems involving angles and distances
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Students studying trigonometry, educators teaching geometry, and anyone seeking to improve their problem-solving skills in mathematical applications involving angles and distances.

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Homework Statement


There is a flag mounted at the top of a building. The angle of elevation from a point 200 ft. to the flagpole's base is 70°, and the angle of elevation from the same point to the top of the flagpole is 82°, find the height of the flagpole.


Homework Equations


Law of Sines? SinA/a = SinB/b



The Attempt at a Solution


I don't really know how to set this problem up...could somebody point me in the right direction? I'm not asking for an answer, just some guidance. Please..
 
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Try make a diagram of the situation. Can you identify any right-angled triangles?
 
Hi AddversitY! :smile:
AddversitY said:
Law of Sines? SinA/a = SinB/b

Nothing so complicated …

you have two right-angled triangles, just use ordinary trig. :wink:​
 

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