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°

Explanation:

Step1: Identify the trigonometric relationship

We have a right - triangle situation where the height on the tree (opposite side to the angle between the wire and the ground) is $a = 10$ feet and the length of the wire (hypotenuse) is $c=12$ feet. We use the sine function $\sin\theta=\frac{a}{c}$.

Step2: Calculate the sine of the angle

Substitute $a = 10$ and $c = 12$ into the sine formula: $\sin\theta=\frac{10}{12}=\frac{5}{6}\approx0.8333$.

Step3: Find the angle

We know that $\theta=\sin^{- 1}(0.8333)$. Using a calculator, $\theta=\sin^{-1}(0.8333)\approx56.4^{\circ}$.

Answer:

$56.4^{\circ}$