A roller coaster travels 101 ft at an angle of
45.7
◦
above the horizontal
How far does it move vertically
To determine how far the roller coaster moves vertically, we need to find the vertical component of the distance traveled.
We can use trigonometry to break down the distance into its horizontal and vertical components. In this case, the angle given is 45.7 degrees above the horizontal.
Using the trigonometric function sine, we can find the vertical component using the formula:
Vertical distance = Distance traveled * sin(angle)
Given that the roller coaster travels 101 ft and the angle is 45.7 degrees, we can substitute the values into the formula:
Vertical distance = 101 ft * sin(45.7 degrees)
To calculate this, convert the angle from degrees to radians:
45.7 degrees * π/180 = 0.797 radians
Now substitute the value into the formula:
Vertical distance = 101 ft * sin(0.797 radians)
Using a scientific calculator, evaluate the sine of 0.797 radians:
sin(0.797 radians) ≈ 0.709
Now we can calculate the vertical distance:
Vertical distance ≈ 101 ft * 0.709
Vertical distance ≈ 71.609 ft
Therefore, the roller coaster moves vertically approximately 71.609 feet.