Having trouble understanding word probl Trig.

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SUMMARY

The discussion revolves around solving a trigonometric word problem involving the height of a rock based on angles of elevation. The angles provided are 16.7 degrees from point A and 24.1 degrees from point B, which is 168 meters closer to the rock. The confusion arose from misinterpreting the distances between points A, B, and C. The correct interpretation clarifies that the distance BC is not 168 meters less than AB, but rather that BC is the unknown distance x, while AC is the total distance from point A to the base of the rock.

PREREQUISITES
  • Understanding of basic trigonometry concepts, specifically angles of elevation.
  • Familiarity with right triangle properties and relationships.
  • Ability to interpret word problems and translate them into mathematical equations.
  • Knowledge of solving for unknowns using trigonometric functions.
NEXT STEPS
  • Study the Law of Sines and Cosines for solving non-right triangles.
  • Practice additional trigonometric word problems to reinforce understanding.
  • Learn how to use tangent functions in real-world applications.
  • Explore graphical methods for visualizing trigonometric problems.
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Students studying trigonometry, educators teaching math concepts, and anyone looking to improve their problem-solving skills in geometry and trigonometry.

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Homework Statement


rock rises straight upward frim the valley floor. From one point the angle of elevation of the top of the rock is 16.7 deg. From a point 168 m closer to the rock the angle of elevation of the top of the rock is 24.1 deg. How high is the rock...

I added an attachment... What I thought was correct I did in red... but the way my solution guide had it is in black... I don't understand how their way works.. can some one please help me understand... thank you...

If I understand this, this will help me understand all the other word problems that are similar... I would appreciate it.. thank you.

Homework Equations





The Attempt at a Solution

 

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Oh yes, the part in red is completely wrong. Imagine you are standing at the vertex of the 16.7° angle of elevation (which I will call point A). When it says "from a point 168 m closer to the rock," you walk to the right (according to your diagram), 168 m closer to the base of the rock (which I will call point C). Now you are at the vertex of the 24.1° angle of elevation (which I will call point B). That is why the distance between A and B (the two vertices) is 168 (in black) and not x (in red). For some reason you're thinking that the distance BC is 168 m less than the distance AB, and that is not correct. The distance BC is 168 m less than the distance AC. And since we don't know the distance BC, we call it x (in black).
 
Thank you.. I understand now... thanks a lot!
 

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