A commonly accepted angle of elevation for safe, accessible wheelchair ramps is 4:5 degrees. The public library's main door is 1:2 m above street level. What will be the run of this ramp?
To find the run of the ramp, we need to use the angle of elevation and the height difference between the street level and the library's main door.
First, let's convert the angle of elevation from a ratio to degrees. The given angle of elevation is 4:5 degrees. We can calculate it by dividing 4 by 5 and then finding its inverse tangent (arctan).
Angle of elevation = arctan(4/5) = 38.66 degrees (rounded to two decimal places)
Now, let's use the trigonometric relationship between the angle of elevation, the height difference, and the run of the ramp:
tan(angle of elevation) = height difference / run
We know the angle of elevation (38.66 degrees) and the height difference (1:2m), and we need to find the run.
Rearranging the formula, we have:
run = height difference / tan(angle of elevation)
Substituting the given values, we get:
run = (1/2) / tan(38.66 degrees)
To calculate this, use a calculator or a scientific calculator app, and make sure it is set to degrees mode. The result will be the run of the ramp in meters.
To find the run of the ramp, we will first calculate the rise, and then use the angle of elevation and the rise to find the run.
Given:
Angle of elevation: 4:5 degrees
Rise (height above street level): 1:2 m
Step 1: Calculate the rise using the given height of the main door.
Since the main door is 1:2 m above street level, the rise is 1 meter.
Step 2: Use the rise and angle of elevation to find the run.
The ratio of the angle of elevation is 4:5 degrees, which can be simplified as 4/5.
We can use the tangent function to calculate the run. The tangent of an angle is equal to the opposite side (rise) divided by the adjacent side (run).
Tangent of the angle = Rise / Run
tan(4/5 degrees) = 1 / Run
To isolate the run, we can take the reciprocal of tangent:
Run = 1 / tan(4/5 degrees)
Using a scientific calculator or online calculator, we can calculate the run as follows:
Run = 1 / tan(4/5) = approximately 14.03 meters.
Therefore, the run of the ramp should be approximately 14.03 meters.