math

posted by on .

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 - ,

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 - ,

Hi - How did you get 45 degrees? Think that's the part I'm lost with.

• math - ,

The angle between west and northwest is 45 degrees, halfway from west to north

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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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Label and sketch the triangle as I did. You will see that the angle between ao and ou is 45 degrees