Roger fastens a rope to the ground that extends from a pole that has been placed in the ground. The rope is 8 feet long, and the pole is 5 feet tall. Using the inverse of sine, what is the angle formed where the rope is fastened to the ground? Round your answer to the nearest whole degree. the answer is not 37
To find the angle formed where the rope is fastened to the ground, we can use the inverse sine function.
Let θ be the angle formed where the rope is fastened to the ground.
We can use the trigonometric relationship sin(θ) = opposite/hypotenuse.
Since the rope is fastened to the ground, the opposite side is the height of the pole, which is 5 feet.
The hypotenuse is the length of the rope, which is 8 feet.
Therefore, we have sin(θ) = 5/8.
To find θ, we can take the inverse sine of both sides: θ = arcsin(5/8).
Using a calculator, we find that arcsin(5/8) ≈ 37.8 degrees.
Rounded to the nearest whole degree, the angle formed where the rope is fastened to the ground is 38 degrees.