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. The sine of an angle is equal to the length of the opposite side divided by the length of the hypotenuse.
In this scenario, the opposite side 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 have sin(angle) = 5/8.
To find the angle, we take the inverse sine of both sides of the equation: angle = arcsin(5/8).
Using a calculator, the approximate value of arcsin(5/8) is 42.47 degrees.
Rounding this to the nearest whole degree, the angle formed where the rope is fastened to the ground is 42 degrees.