Trigonometry Practice Problems: Finding Distances and Angles

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SUMMARY

The discussion focuses on solving trigonometry problems related to finding distances and angles between two towns, W and Y. The calculations provided include determining the hypotenuse using the sine function, finding an angle using the cosine function, and calculating the length of the opposite side using the Pythagorean theorem. The final answers are 38 km for the hypotenuse, approximately 45° for the angle, and 27 km for the opposite side. Participants express uncertainty about the accuracy of the last answer due to the diagram's lack of scale.

PREREQUISITES
  • Understanding of basic trigonometric functions (sine, cosine)
  • Familiarity with the Pythagorean theorem
  • Ability to perform inverse trigonometric calculations
  • Knowledge of angle measurement in degrees
NEXT STEPS
  • Review the Law of Sines and its applications in triangle problems
  • Learn about the Law of Cosines for non-right triangles
  • Explore trigonometric identities for simplifying calculations
  • Practice creating accurate diagrams with scale for trigonometric problems
USEFUL FOR

Students studying trigonometry, educators teaching geometry, and anyone looking to improve their problem-solving skills in distance and angle calculations.

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Homework Statement



As per the attachment


The Attempt at a Solution



for
a) sin58° = 32/hyp
hyp*sin58°=32
hyp=32/sin58°
hyp=32/0848
hyp=37.73
so to the nearest km between towns W & Y = 38km

b)cosθ=adj/hyp
cosθ=27/38
cosθ=0.710
θ=cos^-1(0.710)
θ=44.76

so to the nearest degree the angle = 45°

c)?^2=38^2-27^2
=√715
=26.73

so to the nearest km = 27km

do these look correct? I'm not sure with the last answer as if it is 27km its the same size as the other side and that does not look correct.
 

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Your answers look correct to me.
 
ap123 said:
Your answers look correct to me.

that last one just doesn't feel right, it look noticeably shorter than the known 27 km side
 
eddievic said:
that last one just doesn't feel right, it look noticeably shorter than the known 27 km side

It looks a little shorter, but how accurate is the diagram?
 
ap123 said:
It looks a little shorter, but how accurate is the diagram?

true, it does not show any scale so it probably is correct maybe me overthinking it.
 
eddievic said:
true, it does not show any scale so it probably is correct maybe me overthinking it.

I think it's just the diagram - e.g. the right angle at the bottom is not accurate.
 

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