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
To find the angle formed between the light strand and the pole, we can use trigonometry. We want to find the angle opposite the height of the pole (9 feet) and the hypotenuse of the right triangle formed by the pole and the light strand.
Using the inverse sine function, we have:
sin(angle) = opposite/hypotenuse
sin(angle) = 9/16
To find the angle, we can take the inverse sine of both sides:
angle = sin^(-1)(9/16)
angle ≈ 34.8 degrees
Therefore, the angle formed between the light strand and the pole is approximately 34.8 degrees.