# Homework Help: Trigonometry question

1. May 21, 2013

### eddievic

1. The problem statement, all variables and given/known data

As per the attachment

3. 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

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.

#### Attached Files:

• ###### Trig.docx
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2. May 21, 2013

### ap123

3. May 21, 2013

### eddievic

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

4. May 21, 2013

### ap123

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

5. May 21, 2013

### eddievic

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

6. May 21, 2013

### ap123

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