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

90°
90°

45°
45°

51°
51°

39°

Answer 1

To find the angle formed between the ground and the rope using the inverse sine function, we can use the sine definition in a right triangle context. The setup is as follows:

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

We can use the formula for sine:

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

Substituting the given values:

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

To find the angle θ, we take the inverse sine (arcsin) of \( \frac{7}{9} \):

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

Calculating \( \arcsin\left(\frac{7}{9}\right) \):

Using a calculator:

\[ \theta \approx 51.06° \]

Therefore, rounding to the nearest whole number, the approximate angle formed between the ground and the rope is:

51°

So the correct response is:

51°