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°

90°
90°

39°
39°

Answer 1

To find the angle formed between the ground and the rope, we can use the sine function. We have the height of the pole (7 feet) and the length of the rope (9 feet).

Using the sine function:

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

In this case:

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

So we have:

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

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

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

Now we can calculate \( \theta \):

Using a calculator:

\[ \theta \approx \arcsin(0.7778) \approx 51^\circ \]

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