# Law of cosines

• Feb 24th 2008, 02:22 AM
kri999
Law of cosines
okay i dont know why, this may be extremely easy but i'm just not getting the right answer :(

Here's the question:
richmond is 200 kilometers due east of Teratown and Hamilton is 150 kilometers directly north of Teratown. Find the shortest distance in kilometers between Hamilton and Richmond.

I use law of cosines right? and so what would the equation look like?
• Feb 24th 2008, 02:27 AM
mr fantastic
Quote:

Originally Posted by kri999
okay i dont know why, this may be extremely easy but i'm just not getting the right answer :(

Here's the question:
richmond is 200 kilometers due east of Teratown and Hamilton is 150 kilometers directly north of Teratown. Find the shortest distance in kilometers between Hamilton and Richmond.

I use law of cosines right? and so what would the equation look like?

Pythagoras' Theorem:

$(200)^2 + (150)^2 = (HR)^2$.
• Feb 24th 2008, 02:34 AM
kri999
but i have to use the law of cosines...how do i do that with this problem? or is just not possible?
• Feb 24th 2008, 02:37 AM
mr fantastic
Quote:

Originally Posted by kri999
but i have to use the law of cosines... Mr F asks: Why?

how do i do that with this problem? or is just not possible?

OK:

$
(HR)^2 = (200)^2 + (150)^2 - 2(200)(150) \cos(90^0) = .....
$

In case you haven't guessed, Pythagoras' Theorem is a special case of the cosine rule.
• Feb 24th 2008, 02:47 AM
kri999
Thank you! I got the same equation but somehow I keep getting the answer wrong, but i just tried a differnet method and it worked out..
yeah i have to use law of cosines because that's what the chapter's on haha

thanks so much!
• Feb 24th 2008, 02:50 AM
angel.white
Quote:

Originally Posted by mr fantastic
OK:

$
(HR)^2 = (200)^2 + (150)^2 - 2(200)(150) \cos(90^0) = .....
$

In case you haven't guessed, Pythagoras' Theorem is a special case of the cosine rule.

I actually didn't know that. I just kinda figured he sat around playing with blocks and rulers for a few weeks until a lightbulb turned on.