A train travels uphill at a 12 degree angle. The train rises 150 from the bottom to the top of the hilL. about how long is the track?
Rise = horizontal distance * tan(θ)
Now
Rise = 150 m (or the proper unit)
angle, θ = 12°
Solve for horizontal distance.
To determine the length of the track, we can use trigonometry. First, let's find the vertical rise in meters using the given angle and height.
The vertical rise (h) can be calculated using the formula:
h = distance × sin(angle),
where h is the rise, angle is the angle of inclination, and distance is the length of the track.
Here, the rise is given as 150 meters, and the angle is 12 degrees. Let's substitute these values into the formula:
150 = distance × sin(12)
To solve for the distance, divide both sides of the equation by sin(12):
distance = 150 / sin(12)
Using a calculator, the approximate length of the track is:
distance ≈ 684.59 meters (rounded to two decimal places).
To find the length of the track, we can use trigonometry. In this case, we have a right triangle formed by the track, the vertical distance traveled (150), and the angle of inclination (12 degrees). We can use the sine function to determine the length of the track.
The sine function relates the opposite side of the triangle (the vertical distance traveled, 150) to the hypotenuse (the length of the track). It is expressed as:
sin(angle) = opposite / hypotenuse
Rearranging the formula, we have:
hypotenuse = opposite / sin(angle)
Substituting the given values, we get:
hypotenuse = 150 / sin(12)
Calculating the value using a calculator or appropriate tools, we find:
hypotenuse ≈ 742.405
Therefore, the length of the track is approximately 742.405 units.