A roller coaster travels 170 ft at an angle of 47.5◦ above the horizontal.

How far does it move horizontally?
How far does it move vertically?
Answer in units of ft

horizontal=170cosTheta

vertical=170 sinTheta

To find how far the roller coaster moves horizontally and vertically, we can use trigonometric functions.

The horizontal distance traveled can be found using the cosine function:

horizontal distance = 170 ft × cos(47.5°)

Calculating this:

horizontal distance = 170 ft × cos(47.5°)
≈ 113.83 ft

So, the roller coaster moves approximately 113.83 ft horizontally.

The vertical distance traveled can be found using the sine function:

vertical distance = 170 ft × sin(47.5°)

Calculating this:

vertical distance = 170 ft × sin(47.5°)
≈ 113.00 ft

So, the roller coaster moves approximately 113.00 ft vertically.

To find out how far the roller coaster moves horizontally and vertically, we can use trigonometry.

Given that the roller coaster travels 170 ft at an angle of 47.5° above the horizontal, we can use the trigonometric functions sine and cosine to determine the horizontal and vertical components of the distance traveled.

The horizontal distance traveled (d_horizontal) can be found using cosine:

cos(angle) = adjacent / hypotenuse

In this case, the adjacent side is the horizontal distance traveled and the hypotenuse is the total distance traveled (170 ft). Rearranging the equation, we have:

horizontal distance = cos(angle) * total distance

Plugging in the values, we have:

horizontal distance = cos(47.5°) * 170 ft

Using a calculator or trigonometric table, we find that cos(47.5°) is approximately 0.673. Therefore:

horizontal distance = 0.673 * 170 ft
horizontal distance ≈ 114.41 ft

So, the roller coaster moves horizontally approximately 114.41 ft.

To find the vertical distance traveled (d_vertical), we can use sine:

sin(angle) = opposite / hypotenuse

In this case, the opposite side is the vertical distance traveled. Rearranging the equation, we have:

vertical distance = sin(angle) * total distance

Plugging in the values, we have:

vertical distance = sin(47.5°) * 170 ft

Using a calculator or trigonometric table, we find that sin(47.5°) is approximately 0.759. Therefore:

vertical distance = 0.759 * 170 ft
vertical distance ≈ 129.03 ft

So, the roller coaster moves vertically approximately 129.03 ft.

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