No idea what the textbook is doing

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SUMMARY

The discussion centers on a discrepancy in a textbook problem involving trigonometric calculations related to a rod's length. The user identifies that the textbook incorrectly assumes the rod's length is 4m instead of the correct 6m. Additionally, the user critiques the use of the sine function in the solution, arguing that the tangent function should be employed due to the unknown hypotenuses of the triangles involved. The correct calculations yield x = 4.04 using the equation d = (6-x)tan50 and d = xtan(3).

PREREQUISITES
  • Understanding of trigonometric functions, specifically tangent and sine.
  • Familiarity with solving equations involving variables and angles.
  • Basic knowledge of geometry related to triangles.
  • Ability to interpret problem statements and identify discrepancies in mathematical problems.
NEXT STEPS
  • Review the properties and applications of the tangent function in trigonometry.
  • Study how to correctly set up and solve equations involving multiple variables.
  • Examine common errors in textbook solutions and how to identify them.
  • Practice solving real-world problems involving trigonometric functions and lengths.
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Students studying trigonometry, educators reviewing textbook accuracy, and anyone involved in solving geometric problems with trigonometric functions.

phospho
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I mean, I used a similar method as they're using, but I didn't get their answer at all. Where did the x-4 come from? (I used x-6), also, I got d = (6-x)tan50 and d = xtan(3) solving this to get x = 4.04
 

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phospho said:
I mean, I used a similar method as they're using, but I didn't get their answer at all. Where did the x-4 come from? (I used x-6), also, I got d = (6-x)tan50 and d = xtan(3) solving this to get x = 4.04

Looks like the book's solution is incorrect on two counts. First, the problem statement has changed at some point to have 6m as the length of the rod, while the solution assumes it's 4m. Second, I don't see how they can use the sine function since the hypotenuse's of the triangles are unknown (and not even labelled). They should use the tan function.
 

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