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)

Question

Responses

51°
51°

45°
45°

39°
39°

90°

Answer 1

To find the angle formed between the ground and the rope, we can use the sine function. First, we note that we can create a right triangle with:

• The height of the pole as the opposite side (7 feet)
• The length of the rope as the hypotenuse (9 feet)

We can use the sine function which is defined as:

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

Substituting in the values we have:

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

To find the angle \(\theta\), we take the inverse sine (arcsin) of the ratio:

\[ \theta = \arcsin\left(\frac{7}{9}\right) \]

Using a calculator:

\[ \theta \approx 51.06^\circ \]

So, the approximate angle formed between the ground and the rope is around 51°.

Therefore, the answer is 51°.