Trigonometry Practice Problems: Finding Distances and Angles

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Homework Help Overview

The discussion revolves around trigonometry problems involving the calculation of distances and angles between two towns, W and Y. The original poster presents their attempts at solving three parts of the problem, utilizing sine and cosine functions to find a hypotenuse and an angle, as well as the length of a side in a right triangle.

Discussion Character

  • Exploratory, Assumption checking, Conceptual clarification

Approaches and Questions Raised

  • The original poster attempts to calculate the hypotenuse and angles using trigonometric ratios, while expressing uncertainty about the validity of their last answer regarding the side length. Participants question the accuracy of the diagram and whether the calculated lengths seem reasonable in relation to each other.

Discussion Status

Some participants affirm the correctness of the original poster's calculations, while others express doubt about the last answer, suggesting that the diagram's accuracy may influence their interpretations. The discussion remains open, with participants exploring the implications of the diagram's scale and accuracy.

Contextual Notes

There is mention of a diagram that lacks a scale, which raises questions about the accuracy of the visual representation in relation to the calculated distances.

eddievic
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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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