A roller coaster travels 101 ft at an angle of
45.7
◦
above the horizontal.
How far does it move horizontally
101 cos 45.7
To find how far the roller coaster moves horizontally, we can use trigonometry. The horizontal displacement can be calculated using the formula:
Horizontal displacement = Distance travelled × cos(angle)
In this case, the distance travelled is given as 101 ft and the angle is given as 45.7°.
First, we need to convert the angle from degrees to radians since trigonometric functions in most programming languages use radians. To convert degrees to radians, we can use the formula:
radians = degrees × (π / 180)
Converting 45.7° to radians:
radians = 45.7 × (π / 180) ≈ 0.797
Now, we can calculate the horizontal displacement:
Horizontal displacement = 101 ft × cos(0.797) ≈ 101 ft × 0.696 ≈ 70.196 ft
Therefore, the roller coaster moves approximately 70.196 ft horizontally.