Question

To support a tree damaged in a storm, a 12-foot wire is secured from the ground to the tree at a point 10 feet off the ground. The tree meets the ground at a right angle.

At approximately what angle does the wire meet the ground?

33.6°
39.8°
50.2°
56.4°

Answer 1

Let θ be the angle between the wire and the ground. In the right triangle formed, the opposite side is 10 ft and the hypotenuse is 12 ft, so

sin θ = 10/12 = 5/6.

θ = arcsin(5/6) ≈ 56.4°.

Answer: 56.4°.