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

48°
48°

42°
42°

73°
73°

90°
90°

Answer 1

To find the angle between the volleyball pole and the string, we can use trigonometry. The pole acts as one side of a right triangle, the string acts as the hypotenuse, and the distance from the top of the pole straight down to the ground below the end of the string forms the third side.

Let's denote:

• The height of the pole (adjacent side) = 8 feet
• The length of the string (hypotenuse) = 12 feet

We can use the cosine function to find the angle \( \theta \):

\[ \cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}} = \frac{8}{12} \]

Calculating \( \cos(\theta) \):

\[ \cos(\theta) = \frac{8}{12} = \frac{2}{3} \approx 0.6667 \]

Now we can find the angle \( \theta \) by taking the inverse cosine (arccos):

\[ \theta = \arccos(0.6667) \]

Calculating \( \theta \):

\[ \theta \approx 48^\circ \]

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