Jamal 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. the answer is not 29.5 or 28.1
To solve this problem, we can use trigonometry.
Let's call the angle formed between the light strand and the pole "x".
We can set up a right triangle with the pole as the vertical side and the light strand as the hypotenuse.
The vertical side (pole) has a length of 9 feet, and the hypotenuse (light strand) has a length of 16 feet.
Using the trigonometric function sine, we can calculate the angle x:
sin(x) = opposite/hypotenuse
sin(x) = 9/16
To find the value of x, we can take the inverse sine (also known as arcsine) of both sides:
x = arcsin(9/16)
Using a calculator, we find that the value of x is approximately 35.3 degrees.
Therefore, the angle formed between the light strand and the pole is approximately 35.3 degrees.