In Rochester parking garage, the levels are 23 feet apart. Each up-ramp to the next level is 114 feet long. Find the measure of the angle of elevation of the incline for each ramp to the nearest tenth of a degree.
To find the angle of elevation for each ramp, we can use trigonometry. The angle of elevation is the angle between the ramp and the horizontal ground. In this case, the horizontal distance is given as 114 feet, and the vertical distance is 23 feet.
The tangent of an angle is equal to the ratio of the opposite side to the adjacent side. In our case, the opposite side is the vertical distance, which is 23 feet, and the adjacent side is the horizontal distance, which is 114 feet. Therefore, we have:
tan(angle) = 23/114
To find the angle itself, we need to take the inverse tangent (arctan) of both sides of the equation:
angle = arctan(23/114)
Using a calculator, we can find the arctan of 23/114 to get the angle. Rounding to the nearest tenth of a degree, the angle of elevation for each ramp is approximately 11.5 degrees.