You and a friend walk away from a tree in opposite directions each traveling 15 yards. You were walking due east and then turned toward 45 degrees north and walked 8 yards. Your friend was walking due west and turned 40 degrees south and walked 8 yards. Who is further from the tree

2nd friend heading west

Step-by-step explanation:

This is actually pretty easy to explain.

You and a friend are near a tree and decide to walk away from it. At the beggining you walked 15 yards and your friend too, and then, there's the turn of event. You walked 8 yards toward north east, and your friend 8 yards towards south west.

The key to know which is further from the tree is the angle of turning of both. We need to calculate the component in x from both persons, and then, add it to the previous 15 yards. This way we will know who is further.

Let's begin with the 1°, the one who's heading east:

X = 15 + 8 cos45° = 20.66 yards

Now the friend heading west:

X = 15 + 8 cos40° = 21.13 yards

With these results we can conclude that the 2nd friend is further from the tree.

Hope this helps