# math

posted by .

Ajax is 8 km due west of Oshawa. Uxbridge is 16 km NW of Oshawa. How far is it from Ajax to Uxbridge? Explain whether you have enough information to solve this problem.

my answer was 13.856 km but not confident how I found the angle oshawa to begin with. I used Cos Oshawa = a/h = 8/16, cos-1 0.5=60 degrees.

Please confirm if done correctly...many thanks.

math - Damon, Sunday, August 21, 2011 at 2:44pm
angle AOU = 45 degrees
ao = 8
ou = 16

law of cosines

au^2 = ao^2 + ou^2 - 2*ao*ou*cos 45
au^2 = 64 + 256 - 2*8*16 * .707
au^2 = 139
au = 11.8

math - Dee, Sunday, August 21, 2011 at 3:14pm
Hi - How did you get 45 degrees? Think that's the part I'm lost with.

math - Damon, Sunday, August 21, 2011 at 4:16pm
The angle between west and northwest is 45 degrees, halfway from west to north

math - Sunday, August 21, 2011 at 4:51pm
Yes but why is it 45 degrees? I'm dividing 8 into 16 = .5 then cos-1 .5 = 60. Nothing I do is giving me 45 degrees. Hope you get notified when a thread is updated, I'm inclined to repost this incase.

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draw a sketch and you will see that the angle between ao and ou or angle AOU is that between west and northwest or 45 degrees

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Like try this calculator. You have SAS (side, angle, side)

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how will I see that the angle is 45 degrees? Don't we have to calculate that? This is what I'm asking you about. How is <O calculated so it comes up to 45 degrees?

I have 2 sides and have to find the angle as it's not given before I can proceed to find the third side. I'm asking how you got 45 so I can understand where I went wrong. Thanks for recommending google...that was very helpful in providing clarity to this particular question.

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one side goes west
the second side goes north west, 45 degrees clockwise from the first side.
There is no calculation of 45 degrees. It is given by saying west and northwest

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Ahhh...I see! Thank you for helping, I would have never have worked this out correctly.