SOLUTION: 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 ans

Question 483951: 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.

Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
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.
:
This does not form a right triangle, however we know that the angle at Oshawa is 45 degrees, (NW with W forms a 45 degrees)
:
Let this angle be A, then a = the dist from Ajax to Uxbridge
Using the law of cosine to find a
a^2 = b^2 + c^2 - 2bc*cos(A)
where
a = dist from Ajax to Uxbridge
b=8
c=16
A=45
:
a^2 = 8^2 + 16^2 - 2(8*16)*cos(45)
a^2 = 64 + 256 - 2(128)*.707
a^2 = 320 - 256*.707
a^2 = 320 - 181
a =
a = 11.79 km
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