To get to her friend's house, Sandra walked along the sidewalk in her neighborhood. If she walked 100 yards at a direction of 45° northeast and then turned to walk 400 yards straight east, how many yards and in what direction would she need to walk if she wanted to walk straight home without having to make any turns?

Question

Reiny · Answer

Did you make your sketch?
On mine, I have a triangle with sides 100 and 400 and the contained angle of 135°
Using the cosine law:
x^2 = 100^2 + 400^2 -2(100)(400)cos135°
x = 475.992..

To get the angle opposite the side of 400:
sinØ/400 = sin135/475.992..
sinØ = .5942..
Ø = 36.46°

so the angle should be 45-36.46 = appr 8.54° north of east

Rachel · Answer

Thanks. All of this was right except it was southwest instead of northeast.