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)

Question

Responses

42°
42°

73°
73°

48°
48°

90°
90°

Answer 1

To find the angle formed between the pole and the string, we can use the trigonometric function tangent, which is defined as the opposite side divided by the adjacent side in a right triangle.

In this scenario:

• The height of the pole (which serves as the opposite side of the triangle) is 8 feet.
• The length of the string (which acts as the hypotenuse) is 12 feet.

We need to find the angle that the string makes with the vertical pole. To find the angle θ, we can use the sine function as follows:

\[ \sin(θ) = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{8}{12} = \frac{2}{3} \]

Now we can calculate the angle θ:

\[ θ = \sin^{-1}(\frac{2}{3}) \]

Using a calculator to find the inverse sine:

\[ θ \approx 41.81° \]

Rounding to the nearest degree gives us approximately 42°. Therefore, the angle formed between the pole and the string is approximately 42°.

So the correct answer is: 42°