Question

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)
• 42°
073°
0 480
• 90°

Answer 1

To find the angle formed between the pole (which is 8 feet tall) and the string (which is 12 feet long), we can use the sine function from trigonometry.

We have a right triangle where:
- One side (the height of the pole) is 8 feet,
- The hypotenuse (the length of the string) is 12 feet.

To find the angle \( \theta \) between the pole and the string, we can use the formula:

\[
\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{8}{12}
\]

Calculating this gives:

\[
\sin(\theta) = \frac{2}{3} \approx 0.6667
\]

Now we can find the angle \( \theta \) using the arcsine function:

\[
\theta = \arcsin(0.6667) \approx 42°
\]

Therefore, the approximate angle formed between the pole and the string is **42°**.

So the answer is **42°**.