A 25-foot rope is tied to the top of a 8-foot vertical pole. If the rope is pulled tight what is the angle of elevation formed between the rope and the ground? Write the equation and solve showing all of your work to support your answer. Round your answer to the nearest tenth.
To find the angle of elevation formed between the rope and the ground, we can create a right triangle using the rope, the pole, and the ground.
Let x be the angle of elevation. The vertical leg of the triangle has a length of 8 feet (the height of the pole), and the hypotenuse of the triangle, the rope, has a length of 25 feet.
Using trigonometry, we can set up the equation:
sin(x) = opposite/hypotenuse
sin(x) = 8/25
To solve for x, we need to find the arcsine of 8/25:
x = arcsin(8/25)
x ≈ 18.4 degrees
Therefore, the angle of elevation formed between the rope and the ground is approximately 18.4 degrees.