Pythagorean Theorem: Suppose you travel north for 65 km, and

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cakers44

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Oct 11, 2006
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Suppose you travel north for 65 kilometers, and then travel east 75 kilometers. How far are you from your starting point?

Using the Pythagorean Theorem, I come up with the following:

c^2 = a^2 + b^2
75^2 = 65^2 + b^2
75^2 - 65^2 = b^2
5265 - 4225 = b^2
1040 = b^2

Now what? How do I find b?
 
I was looking at the problem again, and realized I drew the triabgle wrong in my head, so now I get the folloiwing:

c^2 = a^2 + b^2
c^2 = 75^2 + 65^2
c^2 = 5625 + 4225
c^2 = 9850

but that doesn't come out right, either. What am I dong wrong?
 
cakers44,

I was looking at the problem again, and realized I drew the triabgle wrong in my head, so now I get the folloiwing:

c^2 = a^2 + b^2
c^2 = 75^2 + 65^2
c^2 = 5625 + 4225
c^2 = 9850 don't forget to take the square root of both sides to get 'c'.
Right now you have the answer for c^2 not 'c'.
Everything else looks good!
but that doesn't come out right, either. What am I dong wrong?
 
Hi - that is exactly my problem. the square root of 9850 comes out to be:

99.2471662

That can't possibly be right!
 
If you travel 65 north and 65 south, how far are you from where you started?

Let the arithmetic talk for you. Your impression is not nearly so important as your correct result.

Depending on the direction of each, you can get anything from

65+75 = 140

to

75 - 65 = 10

From those two trips.

99ish seems fine.
 
Hi, Liz.
It just seems strange a strange number to be the answer to "how far are you from the starting point". Are you saying it's correct?
 
The hypoteneuse of a triangle isn't always a nice whole number.

\(\displaystyle \L\\\sqrt{75^{2}+65^{2}}=5\sqrt{394}\approx{99.247}\)
 
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