Trigonometry Practice Problems: Finding Distances and Angles

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The discussion revolves around solving trigonometry problems related to distances and angles between two towns, W and Y. The calculations for the hypotenuse and angles were performed, yielding a distance of approximately 38 km and an angle of 45°. However, there was uncertainty regarding the calculation of the third side, which was found to be about 27 km, as it seemed inconsistent with the diagram. Participants noted the lack of scale in the diagram, suggesting that the perceived discrepancies might stem from inaccuracies in the visual representation. Overall, the answers were generally deemed correct, with concerns primarily focused on the diagram's accuracy.
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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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