Final answer:
The angle of elevation can be found by calculating the inverse tangent (arctan) of the ratio of the height of the roller coaster to the length of the track, which for a 305 m rise over a 415 m distance gives the angle when calculated using a calculator in degree mode.
Step-by-step explanation:
To find the angle of elevation of a roller coaster track 415 m long with a height difference of 305 m, you can use the formula for the tangent of the angle, which is the opposite side over the adjacent side in a right triangle. Here, the opposite side is 305 m (height) and the adjacent side is the length of the track, 415 m. You then take the inverse tangent (or arctan) of this ratio to find the angle.
First, calculate the ratio:
opposite/adjacent = 305 m / 415 m
Then, find the angle:
angle = arctan(opposite/adjacent)
You would use a calculator to find:
angle = arctan(305/415)
This will give you the angle of elevation in degrees. Ensure your calculator is set to degree mode before calculating.