Question

Jessica sets up a volleyball net in her backyard. To secure the net in place, she extends a rope from the top of each of the two poles at a diagonal to the ground. Once the poles are placed in the ground, they are 7 feet tall; the rope she uses is 9 feet long. Using the inverse of sine, what is the approximate angle formed between the ground and the rope? (1 point)
0 51°
• 39°
0 90°
• 45°

Answer 1

To find the angle formed between the ground and the rope, we can use the inverse sine function.

Let’s define the elements of the problem:

- The height of the pole (opposite side) = 7 feet
- The length of the rope (hypotenuse) = 9 feet

We want to find the angle \( \theta \) between the ground (adjacent side) and the rope, which can be calculated using the inverse sine function based on the opposite and hypotenuse.

The formula is:

\[
\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{7}{9}
\]

Now we can find \( \theta \):

\[
\theta = \sin^{-1}\left(\frac{7}{9}\right)
\]

Calculating this gives:

\[
\theta \approx \sin^{-1}(0.7778) \approx 51.06^\circ
\]

Therefore, the approximate angle formed between the ground and the rope is **51°**.