Question

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?(1 point) Responses 48° 48° 42° 42° 90° 90° 73°

Answer 1

To find the angle between the pole and the stability string, we can use trigonometry. The scenario forms a right triangle where:

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

We can use the sine function to find the angle θ:

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

This simplifies to:

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

Next, we need to find the angle \( \theta \) by taking the inverse sine (arcsin) of \( \frac{2}{3} \):

\[ \theta = \arcsin\left(\frac{2}{3}\right) \]

Using a calculator, we find:

\[ \theta \approx 42° \]

So, the approximate angle formed between the pole and the string is 42°.