Trigonometry: finding the distance between cities

[killotin]

I took my first trig class yesterday and I already have homework and questions.

I have to find the distance on the surface of the earth between two cities:

San Francisco is at 37 degrees 30 minutes N
Seattle is at 47 degrees 40 minutes N

So far I subtracted the distance between the two and got 14 degrees and 10 minutes N. I changed it to decimal form 14.166

I'm placing it in S=2(3.14159265)(14.166)/(360)(3960mi)

I end up with a number that doesn't correspond with my practice sheet answer.

What am I doing wrong?

 

[soroban]

Re: Trigonometry

Hello, killotin!

Your subtraction is off . . . and your equation is incorrect.

I have to find the distance on the surface of the earth between two cities:
. . San Francosco 37°30' N and Seattle 47°40' N

The difference is: \(\displaystyle \,47^o40'\,-\,37^o30' \:=\:10^o10'\)

The length of arc is given by: \(\displaystyle \L\:\frac{S}{2\pi R}\:=\:\frac{\theta}{360^o} \;\;\Rightarrow\;\;S\:=\:\frac{\pi R\theta}{180}\)

We have: \(\displaystyle \theta\:=\:10\frac{1}{6} \:=\:\frac{61}{6}\)

Therefore: \(\displaystyle \L\:S \:=\:\frac{\pi(3960)(\frac{61}{6})}{180} \:\approx\:702.67\text{ miles.}\)

 

[killotin]

Oh right!

I see my problem from the start. I copied down my question incorrectly on my sheet but typed it up correctly on here. Thanks!