Question

Having completed another stimulating school day, Michael and Alyssia both leave at the same time. They walk together for a while and then go their separate ways. These paths make a 60° angle with one another. Michael toddles along at 2ft/sec, while Alyssia speeds off at 3ft/sec. How far apart are they after 2 minutes?

Answer 1

after t seconds, Michael has gone 2t ft and Alyssa has gone 3t feet.

So, the distance z between them using the law of cosines, is found using

z^2 = (2t)^2 + (3t)^2 - 2(2t)(3t)cos60°

so, plug in your time (in seconds!) and find z.

Answer 2

z^2 = 240^2 + 360^2 - 2(240)(360)cos60°
z^2 = 100800
z = 317.5

Is this correct?