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

39°
39°

90°
90°

45°
45°

51°
51°

Answer 1

To find the angle formed between the ground and the rope, we can use the sine function. The setup can be visualized as a right triangle where:

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

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

Next, we can find the angle \(\theta\) using the inverse sine function:

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

Calculating this gives us:

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

Rounding to the nearest number from the provided options, we find:

51°

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