to support a tree damaged in a storm, a 12 - foot wire is secured from the ground to the tree at a point 10…

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°

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

Explanation:

Step1: Identify the trig - ratio

We have a right - triangle where the height on the tree (opposite side to the angle we want to find) is $a = 10$ feet and the length of the wire (hypotenuse) is $c=12$ feet. We use the sine function since $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$. $\sin\theta=\frac{10}{12}=\frac{5}{6}$

Step2: Find the angle

We need to find $\theta$ such that $\sin\theta=\frac{5}{6}$. So, $\theta=\sin^{- 1}(\frac{5}{6})$. $\theta=\sin^{-1}(\frac{5}{6})\approx56.4^{\circ}$

Answer:

$56.4^{\circ}$