Part A: Rollin’ On
This week’s discussion is an opportunity to investigate the many ways that the concept of “slope” and “angle” touch our daily lives.
In this week’s lessons you will learn about some characteristics of lines and curves. Your discussion forum exercise this week is to apply the concepts of angle of inclination, slope, and rate of change, to everyday examples.
Measure the slope of something where a specific value of slope or a range of values for slope serve a useful function. For example, the slopes of a wheelchair ramp or a handrail are functionally useful. Additionally, the range of steepness (slopes) for wheelchair ramps and handrails is subject to OSHA regulations and building codes.
You can measure the rise and run for a slope physically i.e. by using a tape measure or ruler. Or you can take a picture of something, draw a line along its slope, and make measurements on the picture to calculate the slope.
To-Do:
For this part of exercise do the following:
Measure or calculate the slope of something where the sloping side serves a purpose and is not just decorative or incidental. Use your imagination.
Now upload the measurement you made, along with a picture of the object you found, and tell us what is the slope of the object in that picture.
Express the slope as a ratio (rise/run).
On your picture, mark the angle associated with the slope that you calculated and then determine the value of the angle by using the relationship below. Tell us the value of the angle.
angle = tan-1(slope)
What did you learn from measuring the slopes of physical things?
You will find the inverse tangent (arctan or tan-1) function on many calculators (Desmos, for instance).
Please – no pictures of inclined laptop lids!And, please, pretty please, no measurements of the diagonals of rectangles. What is the learning in that? (Besides, I won’t give you any points for it).