Question

In 2 to 4 complete sentences or steps explain the answer to the following question.


A roller coaster travels 80 ft of track from the loading zone before reaching its peak. The horizontal distance between the loading zone and the base of the peak is

50 ft. At what angle, to the nearest degree, is the roller coaster rising?

Answer 1

To find the angle at which the roller coaster is rising, we can use the trigonometric function tangent, which is defined as the ratio of the opposite side (the vertical rise) to the adjacent side (the horizontal distance). In this case, we can first find the vertical rise using the Pythagorean theorem: \( \text{rise} = \sqrt{80^2 - 50^2} \), which gives us a rise of approximately 60 ft. Then, we can calculate the angle using the formula \( \theta = \tan^{-1}\left(\frac{\text{rise}}{50}\right) \), resulting in an angle of approximately 53 degrees when rounded to the nearest degree.