A roller coaster travels 101 ft at an angle of
56.8� above the horizontal. How far does it move horizontally?
101 cos56.8 = 55.3 feet
To find how far the roller coaster moves horizontally, we can use trigonometry.
The given information is:
Vertical distance traveled (Height) - 101 ft
Angle of inclination above the horizontal - 56.8 degrees
Let's define the variables:
Horizontal distance traveled (Distance) - unknown
Vertical distance traveled (Height) - 101 ft
Angle of inclination above the horizontal (θ) - 56.8 degrees
Now, we can use the trigonometric function cosine (cos) to find the horizontal distance:
cos(θ) = Adjacent / Hypotenuse
In this case, the adjacent side is the horizontal distance traveled, and the hypotenuse is the distance the roller coaster moves at an inclined angle (101 ft).
Substituting the values into the equation:
cos(56.8°) = Distance / 101 ft
To solve for Distance, we can rearrange the equation:
Distance = cos(56.8°) * 101 ft
Using a calculator or trigonometric table, we find:
cos(56.8°) ≈ 0.5591
Substituting this value into the equation:
Distance ≈ 0.5591 * 101 ft
Calculating this, we find:
Distance ≈ 56.6 ft
Therefore, the roller coaster moves approximately 56.6 ft horizontally.