You and a friend decide to set up a volleyball net in your backyard. Each pole that holds the net has a string to secure it to the ground for stability. If the pole is 8 feet tall after being placed in the ground and the stability string is 12 feet long, what is the approximate angle formed between the pole and the string?(1 point)

Question

Responses

42°
42°

90°
90°

73°
73°

48°

Answer 1

To find the angle formed between the pole and the stability string, we can use the trigonometric function tangent, which is defined as the ratio of the opposite side to the adjacent side in a right triangle.

In this case, the height of the pole is the opposite side (8 feet), and the distance from the pole to the point where the string is anchored is the adjacent side. However, we can also use the cosine function since we know the length of the string and the height of the pole.

We can find the angle with the cosine function:

\[ \cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}} \]

Here:

• The adjacent side is the height of the pole: 8 feet.
• The hypotenuse is the length of the string: 12 feet.

Rearranging gives us:

\[ \theta = \cos^{-1}\left(\frac{\text{height of pole}}{\text{length of string}}\right) = \cos^{-1}\left(\frac{8}{12}\right) \]

Calculating:

\[ \frac{8}{12} = \frac{2}{3} \approx 0.6667 \]

Now, we calculate:

\[ \theta \approx \cos^{-1}(0.6667) \approx 48.19^\circ \]

Therefore, the approximate angle formed between the pole and the string is about 48°.

The correct response is:

48°