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?

Given:
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. 

When you visualize the scenario, the 12 foot wire would be the measure of the hypotenuse and the 10 feet off the ground will be the short leg or opposite. The long leg or adjacent is unknown. 

We need to solve for sine theta because the value of hypotenuse and opposite is given.

sin θ = opposite / hypotenuse
sin θ = 10 feet / 12 feet
sin θ = 0.833
θ = 0.83 / sin
θ = 56°

The wire would meet the ground at approximately 56° angle.