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 42 or 37
To find the angle formed where the rope is fastened to the ground, we can use the inverse of sine.
Let's denote the angle formed as θ.
In a right triangle, the sine of an angle is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse. In this case, the side opposite the angle is the height of the pole, which is 5 feet, and the hypotenuse is the length of the rope, which is 8 feet.
So we can write:
sin(θ) = opposite/hypotenuse
sin(θ) = 5/8
Now we can use the inverse of sine to find the value of θ:
θ = sin^(-1)(5/8)
θ ≈ 37.6 degrees
Rounded to the nearest whole degree, the angle formed where the rope is fastened to the ground is 38 degrees.