SOLUTION: Two paths diverge at a 44 degree angle. Two mountain bike riders take separate routes at 6.5 km/hr and 10 km/hr. How far apart are they after 2 hours?

Question 1037267: Two paths diverge at a 44 degree angle. Two mountain bike riders take separate routes at 6.5 km/hr and 10 km/hr. How far apart are they after 2 hours?
Answer by Cromlix(4381) (Show Source): You can put this solution on YOUR website!
Hi there,
Using Cosine Rule:
a^2 = b^2 + c^2 - 2bc Cos A
Setting up a triangle ABC
Angle A = 44 degrees.
Side b = 13 km (2hrs x 6.5 km/hr)
Side c = 20 km (2hrs x 10 km/hr)
Side a is the distance between them
after 2 hours.
a^2 = b^2 + c^2 - 2bc Cos A
a^2 = 13^2 + 20^2 - 2(13 x 20 x Cos(44))
a^2 = 194.94 (2 decimal places)
a = √194.9
a = 13.96 km (2 decimal places)
This is how far they are apart after 2 hours.
Hope this helps :-)
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