Question 205115
Two cyclists leave the corner of State Street and Main Street simultaneously. State Street and Main Street are not at right angles; the cyclists' paths have an angle of 45o between them. How far apart are the cyclists after they each travel 7 miles? Hint: Use the Law of Cosines 
Can you explain how the law of cosines works and how it would apply to this problem? 
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http://hyperphysics.phy-astr.gsu.edu/Hbase/lcos.html

c^2 = 7^2 + 7^2 - 2*7*7*cos(45)
c^2 = 98 - 98sqrt(2)/2
c^2 = 98-49sqrt(2)
c^2 =~ 98 - 69.296
c^2 =~ 28.7
c =~ 5.358