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?

Question

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.

Answer 1

To find the angle formed between the light strand and the pole, we can use trigonometry. The height of the pole can be considered as the opposite side of a right triangle, and the length of the light strand can be considered as the adjacent side.

Using the formula for tangent:

tan(angle) = opposite/adjacent

We can plug in the values:
tan(angle) = 9/16

To find the angle, we take the inverse tangent (arctan) of both sides:

angle ≈ arctan(9/16)

Using a calculator:
angle ≈ 29.5 degrees

Therefore, the angle formed between the light strand and the pole is approximately 29.5 degrees.