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 using inverse sin and solve showing all of your work to support your answer. Round your answer to the nearest tenth.(4 points)
To find the angle of elevation, we can use the inverse sine function.
Let x be the angle of elevation formed between the rope and the ground. We have the following right triangle:
- The opposite side is the height of the pole, which is 8 feet.
- The hypotenuse is the length of the rope, which is 25 feet.
Using the definition of the sine function: sin(x) = opposite / hypotenuse, we have sin(x) = 8 / 25.
To find the angle x, we take the inverse sine of both sides: x = sin^(-1)(8/25) ≈ 18.1 degrees.
Therefore, the angle of elevation formed between the rope and the ground is approximately 18.1 degrees.