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
To solve this problem, we can use trigonometry. We know that the height of the pole is 9 feet and the length of the light strand is 16 feet.
Let's call the angle formed between the light strand and the pole θ. We can use tangent to find this angle.
Tangent(θ) = opposite/adjacent
In this case, the opposite side is the height of the pole (9 feet) and the adjacent side is the length of the light strand (16 feet).
Tangent(θ) = 9/16
To find θ, we can take the arctangent of both sides:
θ = arctan(9/16)
Using a calculator, this gives us:
θ ≈ 28.1 degrees
Therefore, the angle formed between the light strand and the pole is approximately 28.1 degrees.