Trigonometry Practice Problems: Finding Distances and Angles

[eddievic]

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.

 

[ap123]

Your answers look correct to me.

 

[eddievic]

Your answers look correct to me.

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

 

[ap123]

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?

 

[eddievic]

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.

 

[ap123]

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.