A tree is growing on a hill. In an attempt to make the tree grow straight up, a 12-foot-long wire is attached to a tree at a poi
nt 6 feet off the ground. The wire is anchored to the ground 10 feet from the base of the tree. At what angle is the tree growing in relation to the hill?
For this case what we must do is use the law of cosines. We have then: 12 ^ 2 = 6 ^ 2 + 10 ^ 2 - 2 * (6) * (10) cos (x) Clearing we have: cos (x) = (12 ^ 2- (6 ^ 2 + 10 ^ 2)) / (- 2 * (6) * (10)) x = acos ((12 ^ 2- (6 ^ 2 + 10 ^ 2)) / (- 2 * (6) * (10))) x = 93.82 degrees Answer: The tree is growing in relation to the hill at: x = 93.82 degrees
