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

56.4

Explanation:

Answer 2

To calculate the angle α between the wire and the ground we need to find the sine of that angle or sin(α).

We know that sine is the ratio of the length of the opposite side a to the length of hypotenuse c. In our case a=10 feet and c=12 feet.

sin(α)=a/c=10/12=0.8334.

Now we take the inverse sine function to get the angle because: sin⁻¹(sinα)=α.

sin⁻¹(sin(α))=sin⁻¹(0.8334)

α=sin⁻¹(0-8334)=56.44°

So angle α=56.4°