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

Using relations in a right triangle, it is found that the tree meets the wire at an angle of 56.4º.

What are the relations in a right triangle?

The relations in a right triangle are given as follows:

• The sine of an angle is given by the length of the opposite side to the angle divided by the length of the hypotenuse.

• The cosine of an angle is given by the length of the adjacent side to the angle divided by the length of the hypotenuse.

• The tangent of an angle is given by the length of the opposite side to the angle divided by the length of the adjacent side to the angle.

In this problem, we have that:

• The opposite side to the angle is of 10 feet.

• The hypotenuse is of 12 feet.

Hence:

$\sin{\alpha} = \frac{10}{12}$

$\alpha = \sin^{-1}{\left(\frac{10}{12}\right)}$

$\alpha = 56.4^\circ$.

More can be learned about relations in a right triangle at brainly.com/question/26396675
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