You and a friend decide to set up a volleyball net in your backyard. each pole that holds the net has a string to secure it to the ground for stability. if the pole is 8 feet tall after being placed in the ground and the stability string is 12 feet long, what is the approximate angle formed between the pole and the string?

Question

A. 48 degrees
B. 42 degrees
C. 90 degrees
D. 73 degrees

Answer 1

To find the angle formed between the pole and the stability string, we can use trigonometry, specifically the sine function.

We can visualize the situation as a right triangle:

• The height of the pole (8 feet) is the opposite side.
• The length of the stability string (12 feet) is the hypotenuse.

We want to find the angle \(\theta\) formed between the pole and the string. We use the sine function:

\[ \sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{8}{12} \]

Calculating this gives:

\[ \sin(\theta) = \frac{2}{3} \approx 0.6667 \]

Next, we take the inverse sine (arcsin) to find the angle:

\[ \theta = \arcsin(0.6667) \]

Using a calculator, we find:

\[ \theta \approx 41.81 \text{ degrees} \]

Rounding to the nearest degree, we find that the angle is approximately 42 degrees.

So, the correct answer is:

B. 42 degrees