Question 974529: You walk east 720 feet to get from your house to class. After class, you walk southwest 1,044 feet to meet your friends for lunch. When walking the 756 feet back home from lunch, what direction are you traveling?
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! This is a triangle with
E-W leg 720
Then 45 degree angle to go SW 1044 feet
Then unknown angle to go 756 feet home.
Law of Sines problem.
Need angle between 1044 and 756 leg
sin45/746 = sin x/720
cross multiply, and sin x=(509.112/756)
This is 0.6734 and the arc sin is 42.33 degrees.
The supplement of this angle is 137.67 degrees
The direction is 2.67 E of north or N2.67E
For checking, the first and last legs are almost the same, suggesting almost at 45-45-90 triangle, so the angle arriving back is almost a right angle.
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