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Todd and Scott left the dining hall for a walk on two straight paths that diverge by 48°. Scott walked 580 m and Todd walked 940 m. How far apart are they?

Answer 1

Scott and Todd are approximately #700.3"m"# apart.

Let's draw a picture.

From the picture, we can see that the problem is equivalent to finding the length of the third side of a triangle in which the other two sides are length #940# and #580# and their shared angle is #48^@#.

This is the perfect time to use the law of cosines.

If we let #c# be the third side that we are looking for, applying the law of cosines gives us

#c^2 = 940^2 + 580^2 - 2(940)(580)cos(48^@)#

#=> c^2 = 1220000 - 1090400cos(48^@)#

#=> c = sqrt(1220000 - 1090400cos(48^@)) ~~ 700.3#

Thus Scott and Todd are approximately #700.3"m"# apart.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.