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. 
:
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 = {{{sqrt(139)}}}
a = 11.79 km