Question

amal is hanging up Christmas lights in his front yard to mimic the look of a Christmas tree. He starts by placing a pole in the ground and then extending strands of lights from the top of the pole to the ground in a circular pattern. The pole is 9 feet tall once placed in the ground, and each light strand is 16 feet long. If he attaches a strand of lights to the top of the pole and extends it down to the ground, what is the angle formed between the light strand and the pole? Round your answer to the nearest tenth.(1 point) The angle measure is approximately

Answer 1

To find the angle between the strand of lights and the pole, we can use trigonometry. We know the height of the pole (vertical side) is 9 feet, and the length of the light strand (hypotenuse) is 16 feet.

Using the sine function, which is defined as:

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

we can rearrange this to find the angle \( \theta \):

\[ \theta = \sin^{-1}\left(\frac{\text{opposite}}{\text{hypotenuse}}\right) = \sin^{-1}\left(\frac{9}{16}\right). \]

Now, we'll calculate it:

1. Calculate \( \frac{9}{16} \):

   \[ \frac{9}{16} = 0.5625. \]

2. Now, take the inverse sine:

   \[ \theta = \sin^{-1}(0.5625). \]

Using a calculator to find \( \sin^{-1}(0.5625) \):

\[ \theta \approx 34.5^\circ. \]

Thus, the angle formed between the light strand and the pole is approximately:

\[ \boxed{34.5} \]

Rounded to the nearest tenth of a degree.