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 point 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?

The tree segment from its base to the wire attachment is 6 feet, the distance along the hill to the anchor is 10 feet, and the wire is 12 feet. The angle between the tree and the hill is opposite the 12-foot side. By the Law of Cosines, cos θ = (6² + 10² − 12²) / (2·6·10) = −8/120, so θ ≈ 93.8°. The tree therefore makes an angle of 93.8 degrees with the hill.

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